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MEASUREMENT 

OF 

GAS  AND  LIQUIDS 

BY  ORIFICE  METER 


BY 

HENRY   P.  WESTCOTT 

I, 

Author  of    ""  Hand    Book    of    Natural  Gas,"   "Hand  Book   of 

Casmgnead    Gas,     "Measurement    of   Gases   \Vnere 

Density  Changes,"  and  ""Pressure  Extensions." 

ASSISTED  BY 

JOHN   C.  DIEHL 


SECOND    EDITION 
1922 


PUBLISHED     BY 

METRIC    METAL    WORKS 

ERIE,  PENNSYLVANIA 


COPYRIGHTED  1922 

BY  METRIC  METAL  WORKS 


MINING 


PRESS  OF 

ASHBY  PRINTING  CO 
ERIE — PITTSBURGH 


PREFACE 


The  first  edition  of  "Measurement  of  Gas  by  Orifice  Meter" 
published  in  1918  was  the  first  instance  that  we  know  of 
where  the  complete  data  pertaining  to  the  orifice  meter  and 
orifice  measurement  was  presented  in  book  form,  and  it  is 
gratifying  to  both  the  author  and  the  publisher  to  know  that 
the  book  was  received  with  such  favor  as  to  have  exhausted 
the  edition  in  a  comparatively  short  time. 

Due  to  the  universal  need  that  the  first  edition  has  met, 
and  our  desire  to  continue  to  publish  authoritative  infor- 
mation regarding  the  orifice  meter  and  its  varied  uses,  we 
are  pleased  to  present  this  second  edition.  This  edition  has 
been  thoroughly  revised  and  enlarged  giving  more  detailed 
and  complete  information,  including  data  for  the  measure- 
ment of  air,  steam,  water  and  oil. 

The  tables  of  pressure  extensions  contained  in  the  first 
edition  are  omitted  in  this  book,  and  are  now  published  by 
themselves  in  a  book  entitled  "Pressure  Extensions." 

It  is  hoped  that  this  volume  in  its  enlarged  form  may 
further  establish  the  acceptance  of  orifice  meter  measure- 
ment as  a  standard  method  and  assist  both  engineers  and 
laymen  to  a  greater  extent  than  before. 

The  author  and  publisher  again  gratefully  acknowledge 
the  valuable  assistance  rendered  by  the  men  who  helped 
with  the  first  edition  as  well  as  the  assistance  rendered  by 
the  engineers  of  the  Bureau  of  Mines  and  business  associates 
who  have  so  kindly  contributed  to  make  this  second  edition 
more  complete. 

o 


TABLE  OF  CONTENTS 


PAGE 

PREFACE - in 

PART  ONE— GENERAL 

Orifice  Meter 1 

Pitot  Tube  and  Meter 2 

Description  of  first  Pitot  Tube 2 

Pitot  Tube,  Measurement  of  Open  Flow  of  Gas  Well 3 

Oliphant  Pitot  Tube 3 

Portable  Pitot  Tip  and  Box 5 

Pitot  Meter  Installation V,  6 

Pitot  Meter  Operation 6 

Orifice  Meter  and  Differential  Gauge,  History 11 

Differential  Gauges,   Development 13 

"Bomb  Shell"  Type 14 

Adaptability  of  Orifice  Meter 17 

PART  TWO— PHYSICAL  PROPERTIES  OF  FLUIDS 

Fluids !  '•  19 

Theory  of  Constitution  of  Matter 19 

States  of  Matter 19 

Fluids,  Liquids  and  Gases 20 

Vapor 21 

Vapor  and  Gas,  Distinction  between 21 

Critical   Temperatures  and    Pressures   of  Various  Gases 

(Table) 21 

Gravitation 22 

Force  of  Gravity 22 

Fluid  Pressure 22 

Compressibility  and  Expansibility  of  Gases 25 

Expansive  Power  of  Gases 26 

Pascal's  Law 27 

Pressure  and  Liquid  Head 28 

Pressure  Equivalents  (Table) 31 

Pressure  Equivalents,  Mercury,  Water,  Ib.  per  sq.  in 32 

Atmospheric  Pressure 32 

Barometer...  33 


TABLE      OF      CONTENTS 


PART  TWO— PHYSICAL  PROPERTIES  OF 

FLUIDS— Continued  PAGE 

Absolute  Pressure 34 

Atmospheric  Pressure  of  Gas  Fields 35 

Pressure  Gauges 36 

Spring  Gauges 36 

U  Tubes  or  Siphon  Gauges 38 

Static  Pressure 39 

Vacuum 39 

Vacuum — Absolute  Pressure  (Table) 43 

Pressure  Base 44 

Velocity 44 

Uniform  or  varied  motion 45 

Acceleration 45 

Velocity  Head 46 

Fluid  Velocity 47 

Coefficient  of  Velocity 50 

Temperature 51 

Absolute  Temperature 51 

Temperature  Base 52 

Perfect  Gases " , .  .  _  53 

Charles'  Law (  .  53 

Boyle's  Law 55 

Absolute  Temperature — Absolute  Pressure 57 

Law  of  Perfect  Gases 59 

Pressure  Due  to  Head  of  Gas ;*-•'•  62 

Pressure  and  Gas  Heads 63 

Velocity  Head  of  Flowing  Gases. 64 

PART  THREE— ORIFICE  METER  MEASUREMENT 

General  Description 67 

Orifice  Meter  Layout 69 

Orifices 73 

Orifice  Constants  (Table) 75 

Orifice  Meter  Body ?M  76 

Determination  of  Orifice  Coefficients 77 

Coefficients  for  Pipe  Connections 77 

Joplin  Holder  Tests 78 

Derivation  of  Orifice  Meter  Formula  for  Flow  of  Air 79 

Orifice  Meter  Formula  for  Gas 80 

General  Outline ,.  ,i>  82 

Leakage  Tests — Joplin  Holder 83 


TABLE      OF      CONTENTS 


PART  THREE— ORIFICE  METER    MEASURE- 
MENT— Continued  PAGE 

Change  of  Volume  of  Holder  with  Temperature 83 

Procedure  during  Orifice  Tests 91 

Summary  of  Results  of  Tests 94 

Comparison  with  Charlottenburg  Tests 98 

Summary  of  Charlottenburg  and  Joplin  Tests 98 

Erie  Holder  Tests 99 

Erie  Holder 100 

Leakage  Tests 101 

Summary  Erie  Tests 104 

Status  of  Coefficient 106 

Comparison — Joplin,  Wann  Line  and  Erie  Tests 107 

Values  of  Coefficient  of  Velocity  (Diagram) 108-109 

Measuring  Flow  of  Fluids ' 110 

Application  Velocity  Formula  for  Flow  of  Air Ill 

Application  of  Velocity  Formula  for  Flow  of  Gas 112 

Application  of  Velocity  Formula  for  Flow  of  Water 113 

Application  of  Velocity  Formula  for  Flow  of  Oil 114 

Mercury  Float  Type  Differential  Gauges 117 

Sectional  View  of  Differential  Gauge 119 

Temperature  Effect  on  Differential  Gauges 120 

Accuracy  of  Orifice  Meter 121 

Percentage  Variations 123 

Differential  Gauge  Capacities 126 

Differential  Range 126 

Special  Types  of  Gauges 129 

Differential  Gauge,  2J/£  inch  Range 129 

Combination  25  inch  and  100  inch  Differential  Gauge 129 

Indicating  Gauge 130 

Recording   Differential   and   Static   Pressure   and    Tem- 
perature Gauge 132 

Relation  Differential  to  Pressure 132 

Relationship    between    Static    Pressure  and    Location  of 

Orifice 134 

Hourly  Coefficients  for  4  inch  Pipe  (Diagram) 134 

Pressure  Connections  or  Taps 135 

Friction  Loss 136 

Percentage  of  Friction  Loss  to  Differential 136 

Friction  Loss  vs.  Capacity 139 

Pressure  Loss. .  141 


TABLE      OF      CONTENTS 


PART  THREE— ORIFICE  METER   MEASURE- 
MENT—Continued  PAGE 

Pulsating  Flow 143 

Pulsation  vs.  Vibration 145 

Vibration  of  Differential  Pen  Arm 145 

Pulsation 146 

Determination  of  Pulsating  Flow 147 

Instructions  to  Meter  Attendants 152 

Changing  Orifice  Meter  Charts 152 

Testing  Apparatus 154 

Inspectors  Test  Pump  for  Static  Pressure  Gauges 154 

Vacuum  Gauge  Test  Pump 155 

Pocket  Gauge  for  Testing  Differential  Gauges 156 

Siphon  or  U  Gauges 157 

Permanent  Gauges  for  Testing  Differential  Gauges 158 

Portable  Water  Differential  Test  Gauges 159 

PART  FOUR— MEASUREMENT  OF  GAS  AND  AIR 

General  Description 161 

Derivation  of  Coefficients 163 

Coefficient  of  Velocity L  171 

Hourly  Orifice  Coefficients  for  Gas  2^  and  8  Diameter  Con- 
nections.   171 

Atmospheric  Pressure  14.4 173-180 

Atmospheric  Pressure  14.7 181-184 

Specific  Gravity 186 

Multipliers  for  Revision  of  Coefficients 186 

Multipliers  for  Change  of  Pressure  Base 188 

Multipliers  for  Atmospheric  Pressure  Changes 189 

Multipliers  for  Base  Temperature  Changes 191 

Multipliers  for  Changes  of  Flowing  Temperature 192 

Multipliers  for  Specific  Gravity  Changes 193 

Pressure  Base  Multipliers  (Tables) 195 

Multipliers  for  Atmospheric  Pressure  Changes  (Table) .  .  .  196 

Base  Temperature  Multipliers  (Table) 197 

Flowing  Temperature  Multipliers  (Table) 198 

Specific  Gravity  Multipliers  (Tables) 199-200 

Specifications  for  Orifice  Meter  Computations  for  the  Osage 

Nation 202 

Values  of  Cv  for  2^  and  8  Diameter  Connections 208 

Values  of  Cv  for  Flange  Connections 211 


TABLE      OF      CONTENTS 


PART  FOUR— MEASUREMENT  OK  GAS 

AND  AIR— Continued  PAGE 

Hourly  Orifice  Coefficients  for  Gas  and  Air,  pressures  taken 

at  Flanges 213 

Orifice  Capacities  for  Air,  Pipe  Connections 214 

Orifice  Capacities  for  Gas,  Pipe  Connections 215 

Orifice  Capacities  for  Air,  Flange  Connections 216 

Orifice  Capacities  for  Gas,  Flange  Connections 217 

Measurement  of  Gas  in  large  volume 219 

Effect  of  Atmospheric  Pressure  on  Gas  Measurement 221 

Gas  Contracts 230 

Multiple  Orifice  Meter  Installation 236 

Installing  Gas  or  Air  Meters 239 

Orifice  Meter  Installations  for  Measuring  Gases. 241 

Orifice  Meter  Body. 245 

Orifice  Meter  Flanges 245 

Gauge  Line  Connections 245 

Orifice  Meter  for  Coke  Oven  Gas 246 

Installing  Differential  and  Static  Pressure  Gauge 247 

Setting  up  Gauge  ..... ...  ....  ... .  .  . 247 

Differential  Pen  Arm .  247 

Adding  Mercury 247 

Static  Pressure  Connections 248 

By-Pass 248 

Turning  on  Gas  or  Air 249 

Leaks 249 

Orifice  Capacities 249 

Vibrating  Differential  Pen  Arm 250 

Diagrams — Installations  for  Measuring  Gas  or  Air. 251-254 

Testing  Differential  Gauges  for  Measuring  Gas  or  Air 255 

Checking  Gauge  for  Zero 255 

Checking  Differential  Gauge  on  Pressure  Lines 256 

Checking  Differential  Gauge  on  Vacuum  Lines 256 

Checking  Differential  Gauges  under  Working  Pressure 258 

Adjustment 258 

Testing  Static  Spring 258 

Orifice  Meter  Test  Report 259 

Reading  Charts 261 

Orifice  Meter  Calculator 267 

Form  for  Face  of  Envelope  used   for  Filing  Orifice  Meter 

Charts T . . . . : . , ,  270 

ix 


TABLE      OF      CONTENTS 

PART  FIVE— MEASUREMENT  OF  STEAM  PAGE 

General 271 

Derivation  of  Coefficients 273 

Properties  of  Saturated  Steam  (Table) 277 

Hourly  Orifice  Coefficients 282,  287 

Hourly  Capacity  of  Orifice  for  Steam 291-292 

Tests,  Steam  Measurement 294 

Installing  and  Testing  Steam  Meters 296 

Diagrams  of  Installations  for  Measuring  Steam -.  303 

PART  SIX— MEASUREMENT  OF  WATER 

General 307 

Derivation  of  Coefficients 309 

Hourly  Orifice  Coefficients  for  Water 312 

Differential  Pressure  Extensions 313 

Hourly  Capacity  of  Orifices  for  Water 314 

Water  Measurement  Tests 315 

Installing  and  Testing  Water  Meters 316 

PART  SEVEN— MEASUREMENT  OF  OIL 

General 319 

Derivation  of  Coefficients ( .  322 

Hourly  Coefficients  for  Oil 330 

Multipliers  for  Specific  Gravity  and  Viscosity 331 

Hourly  Capacities  of  Orifice  for  Oil 332 

Oil  Measurement  Tests 333 

Installing  and  Testing  Oil  Meters 335 

PART  EIGHT— ORIFICE  CAPACITIES 

General. 341 

Orifice  Capacities  for  Gas,  Pipe  Connections  (Tables) 344-383 

Orifice  Capacities  for  Gas,  Flange  Connections  (Tables) .  .  384-423 

Orifice  Capacity  Diagrams 424-428 

Information  Required  when  Ordering  Meters 425 


PART  ONE 


ORIFICE  METER—  PITOT  TUBE  AND  METER- 
HISTORY  AND  USES  OF  ORIFICE  METERS  AND 
DIFFERENTIAL  GAUGES 

ORIFICE    METER 

During  the  past  decade  no  type  of  volume  measuring 
apparatus  has  received  as  much  attention  as  the  simplest 
form  of  velocity  meter,  the  orifice  meter.  This  type  of 
meter  with  the  differential  gauge  has  proven  to  be  the  most 
accurate  and  dependable  apparatus  designed  for  the  measure- 
ment of  gases  and  liquids  flowing  in  pipe  lines.  It  is  being 
used  successfully  for  measuring  hydrogen,  the  lightest  of 
commercial  gases,  and  hot  tar,  one  of  the  most  viscous  of 
liquids.  The  shape  and  design  of  the  orifices  have  undergone 
minor  changes,  the  main  improvements  have  been  made  in 
the  differential  gauge  which  today  will  indicate  and  record 
readings  within  y^  of  its  total  range  under  pressures  from 
28  inches  of  mercury  vacuum  to  500  Ib.  per  square  inch. 

This  type  of  meter  has  been  recognized  by  the  Courts 
and  State  commissions  as  an  instrument  for  correct  measure- 
ment. It  has  passed  the  acid  test  of  reliability  and  millions 
of  cubic  feet  of  gas  are  paid  for  daily,  according  to  its  records. 

Many  simple  and  complicated  forms  of  velocity  meters 
have  been  designed,  but  up  to  the  present  none  have  ob- 
tained any  advantage  over  the  orifice  except  at  the  expense 
of  those  most  fundamental  qualities,  accuracy  and  depend- 
ability. 

1 


c . 

I  «'>  ?4*.  ««  GENERAL 


PITOT  TUBE  AND  METER 

The  Pilot  Tube  was  first  used  for  measuring  flowing 
streams  of  water  and  only  in  recent  years  has  it  been  applied 
to  measuring  gas. 

As  first  constructed  it  measured  the  velocity  or  impact 
of  the  flowing  water  and  indicated  it  in  a  bent  glass  tube. 
In  its  simplest  form  (Fig.  1)  it  consisted  of  a  bent  tube, 
the  mouth  of  which  was  placed  pointing  upstream  and 
measured  the  impact  or  dynamic  pressure  made  by  the 
flowing  water.  The  water  raised  in  the  vertical  part  of  the 
bent  tube  to-a  height  above  the  surface  of  the  flowing  stream 
and  this  height  h  was  equal  to  the  velocity-head  V2/2g,  so 
that  the  actual  velocity  V  was  practically  equal  to  ^2gh. 
As  constructed  for  use  in  streams,  Pi  tot's  apparatus  consisted 
of  two  tubes  placed  side  by  side  with  their  submerged  mouths 
at  right  angles  so  that  when  one  is  opposed  to  the  current, 
the  other  stood  normal  to  it. 


h 

_L 


Fig.  1— PITOT  TUBE   USED  IN  MEASURING  FLOWING  STREAMS 


Henri  Pitot  (Pe'tot)  the  inventor  of  the  Pitot  Tube, 
was  a  French  Physicist  and  Engineer.  He  was  born  in 
1695,  and  died  in  1771. 

From  the  foregoing  invention  was  evolved  the  method 
commonly  used   to   measure   the  open  flow   of  gas  wells. 

2 


GENERAL 


In  testing  gas  wells  only  one  tube  was  used,  as  the  gas  flowing 
from  a  gas  well  had  a  free  exit  into  the  atmosphere,  and  con- 
sequently had  no  static  pressure. 


Fig.  2—PITOT   TUBE  MEASURING  THE    VOLUME  OF  GAS 
FLOWING  FROM  A   GAS   WELL 

Oliphant  Pitot  Tube— A  rough  sketch  of  the  Pitot  Tube 
as  used  for  the  measurement  of  natural  gas  is  shown  in  Fig.  3. 

The  principles  of  this  tube,  however,  are  identically  the 
same  as  those  used  in  the  more  refined  tube  of  to-day. 
A  was  a  piece  of  s/g  inch  iron  pipe,  L-  shaped  and  inserted 
in  a  4  inch  pipe  so  that  the  open  end  A  came  directly  in 
the  centre  of  the  pipe.  Another  piece  of  straight  %  inch 
pipe  B  was  placed  one  foot  distant  from  the  point  C  on 
the  upstream  side.  On  account  of  the  gas  flowing  against 
the  open  end  A,  the  static  and  dynamic  pressures  were  trans- 
mitted to  the  U  tube,  while  only  the  static  pressure  was 

3 


GENERAL 


transmitted  from  the  point  B.  In  the  U  tube  between  B 
and  C  the  static  pressure  was  counterbalanced  by  itself, 
therefore  it  was  the  dynamic  pressure  which  caused  the 
water  in  the  U  tube  to  rise  to  the  height  h.  This  h  then 


/S///S/S//SS///S/SSS/S/SM^^^ 


Fig   3— 


OF  PITOT  TUBE  USED  IN  MEASURING  FLOWING 
GAS  IN  A  PIPE  LINE 


was  the  height  of  water,  or  pressure  which  would  produce 
the  velocity  V  of  the  gas  flowing  in  the  pipe  line.  The 
static,  or  gauge  pressure  p  was  observed  by  means  of  a 
large  U  tube  filled  with  mercury,  one  column  being  con- 


,  4— SECTIONAL  VIEW  OF  THE  OLIPHANT  PITOT  TUBE,  SHOWING 
SADDLE,  TIP  AND  SECTION  OF  BRASS  TUBE 


GENERAL 


nected  to  the  connection  at  B  and  the  other  column  open 
to  the  atmosphere.  The  Pitot  Tube  was  then  calibrated 
and  the  coefficient  for  it  was  determined  by  passing  gas 
through  it  into  a  large  gas  holder  under  varying  con- 
ditions of  flow  and  pressure.  Other  tubes  were  then 
made  by  comparing  them  to  these  tubes,  and  as  they  proved 
very  successful  it  was  determined  to  make  more  refined 
tubes  of  various  sizes,  and  again  compare  them  with  the  gas 
holder,  thus  providing  what  are  known  as  Standard  Tubes 
with  which  all  other  tubes  are  compared  and  their  co- 
efficients determined. 


Fig.  6— PORTABLE  PITOT  TIP  AND  BOX 

5 


GENERAL 


Portable  Pitot  Tip  and  Box— In  January,  1910,  Mr. 
Oliphant  found  the  need  for  a  Pitot  Tube  that  could  be 
quickly  and  easily  transported  from  place  to  place  in  the 
gas  fields  in  order  to  keep  a  careful  check  on  gas  wells  to 
determine  whether  their  flow  was  diminishing  or  not,  while 
under  working  conditions.  This  brought  about  the  in- 
vention of  the  Pitot  Tip  and  Box  shown  in  Fig.  5. 
In  this  method,  the  Box  was  attached  to  the  pipe  line 
leading  from  the  well  and  when  not  in  use  the  tip  was  with- 
drawn and  the  opening  plugged  with  a  common  pipe  plug. 
Each  line  to  the  different  wells  was  fitted  with  a  similar 
Box  and  the  gauge  was  carried  from  one  location  to  another 
with  little  inconvenience. 

When  measuring  with  this  apparatus  the  regular  pipe 
line  was  used  instead  of  a  12  foot  specially  drilled  brass  tub- 
ing of  the  same  size  as  the  line.  Although  the  error  was 
greater  than  with  the  perfected  Oliphant  Pitot  Tube,  it 
served  its  purpose  to  a  high  degree  of  satisfaction. 

Pitot  Meter  Installation  and  Operation — The  best  results 
with  the  Pitot  Tube  are  obtained  where  it  is  especially  de- 
signed for  permanent  installation,  and  when  properly  built 
and  installed  it  becomes  a  scientific  instrument  of  accur- 
ate measurement.  It  is  constructed  of  a  carefully  made 
steel  tip,  having  a  hole  about  one-quarter  inch  in  diameter, 
inserted  in  the  exact  center  of  a  seamless  drawn  brass  tube 
with  interior  surface  polished  and  gauged  to  accurate  and 
uniform  size  throughout  its  length.  The  tip  is  mounted 
in  a  saddle  in  such  a  manner  as  to  be  easily  removed  for 
cleaning,  and  easily  reinserted  to  occupy  exactly  the  pre- 
vious position.  The  size  of  the  brass  tube  used  is  determined 
by  the  quantity  of  gas  to  be  measured,  and  is  chosen  so  as  to 
produce  a  velocity  much  higher  than  that  in  the  main  pipe 
lines,  in  order  to  produce  a  high  differential  or  impact 
pressure  reading,  thus  greatly  increasing  the  accuracy  of 

6 


GENERAL 


the  instrument  by  diminishing  the  error  of  observation. 
Each  tube  must  be  calibrated  against  a  standard  tube  and 
a  coefficient  obtained,  which,  when  multiplied  by  the  square 
root  of  the  product  of  the  differential  pressure  and  the  static 
pressure  (in  absolute  units),  will  give  the  flow  in  unit  time. 

These  high  precision  tubes  are  usually  installed  in  bat- 
teries of  two  or  more,  for  obtaining  measurements  of  a  wide 
range  of  flows,  and  must  have  a  sufficient  run  of  pipe  of  the 
same  size  as  the  tube,  both  ahead  and  behind  them,  to 
avoid  eddies  and  counter  currents  in  the  flow.  The  polished 
interior  surface  of  the  tube,  and  the  high  velocity  of  the  gas 
prevent  the  formation  of  deposits  and  the  tube  coefficient 
thus  remains  constant  for  a  long  period.  Should  any  acci- 
dent occur  whereby  the  tube  becomes  dented  or  injured  in 
any  way,  it  is  necessary  to  have  it  repaired  and  recalibrated 
to  obtain  a  new  coefficient. 

It  also  should  be  borne  in  mind  that  Pitot  Tube  observa- 
tions must  be  made  every  fifteen  minutes  during  the  twenty- 
four  hours.  This  requires  the  services  of  two  men  working 
twelve  hour  shifts. 

The  ordinary  commercial  Pitot  Tube  should  be  used  with 
caution,  for  in  spite  of  its  extreme  simplicity  it  is  a  delicate 
instrument  and  should  be  handled  as  such.  W;hen  used 
in  ordinary  pipe  lines,  the  velocities  encountered  may 
produce  differential  pressures  so  small  that  it  is  impossible  to 
read  them  with  accuracy,  and  the  interior  surface  of  the  pipe 
may  be  rough  and  uneven,  a  condition  that  seriously  affects 
the  result  obtained  with  the  instrument.  The  internal 
diameter  of  commercial  pipe  is  not  strictly  uniform  and  is 
difficult  to  obtain  with  exactness,  and  as  this  factor  enters 
into  the  Pitot  Tube  formula  as  the  square  of  the  value,  any 
percentage  of  error  in  the  measurement  of  the  diameter 
is  doubled  in  the  effect  upon  the  final  result.  A  further 
difficulty  is  presented  in  the  necessity  of  placing  the  tube  in 

7 


GENERAL 


the  cross  section  of  the  pipe  at  the  point  of  average  velocity, 
which  point  varies  in  the  different  sizes  of  pipe,  and  for  dif- 
ferent conditions  of  interior  surface.  A  better  plan  is  to 
place  the  tip  in  the  center  of  the  pipe  and  use  the  coefficient 
obtained  by  actual  calibration  for  each  size  of  pipe.  If  this 
is  done  and  care  is  taken  to  see  that  the  interior  of  the  pipe 
is  free  from  sediment  or  dirt,  and  its  diameter  where  the  tip  is 
inserted  is  accurately  obtained,  very  satisfactory  results  may 
be  obtained  in  the  field  with  the  Pitot  Tube.  In  all  cases, 
a  free  run  of  at  least  forty  feet  of  pipe  of  the  same  size  as 
that  in  which  the  tube  is  inserted  must  be  installed  on  the 
inlet  side  of  the  tube,  and  ten  feet  on  the  outlet,  and  there 
must  be  no  fittings  or  obstructions  nearer  to  the  tube  than 
these  distances. 

While  the  Pitot  Tube  is  considered  a  very  accurate  meas- 
uring instrument,  its  high  cost  of  installation  and  the  inability 
to  easily  transport  it  from  one  location  to  another  in  the  gas 
field  caused  it  to  be  displaced  by  the  smaller  and  more  easily 
moved  orifice  meter  with  its  self  recording  differential 
gauge. 

The  invention  of  the  recording  differential  gauge  was 
the  direct  result  of  the  objectionable  high  upkeep  of  the  old 
Pitot  Tube,  and  lack  of  ability  to  easily  transport  the  large 
and  cumbersome  instrument  from  one  place  to  another.  The 
recording  differential  gauge  now  does  the  duty  formerly  re- 
quired of  the  employees  working  double  shift,  who  read  the 
water  gauge  every  fifteen  minutes  throughout  the  twenty- 
four  hours  and  made  hand-written  reports  which  had  to  be 
sent  to  the  head  office  daily. 


GENERAL 


GENERAL 


Fig.    7 — ONE    OF    THE    EARLY    DESIGNS    OF    THE   RECORDING 

DIFFERENTIAL    GAUGE  AND  ORIFICE   FLANGE    METER 

KNOWN  AS  THE  "BOMBSHELL"  TYPE 


10 


GENERAL 


HISTORY  AND  USES  OF  ORIFICE  METERS  AND 
DIFFERENTIAL  GAUGES* 

"In  1910  the  demand  for  a  Pitot  tube,  or  meter  based  on 
that  principle,  which  could  be  quickly  changed  and  more 
easily  handled  than  the  heavy,  cumbersome  Pitot  tubes, 
developed.  To  meet  this  need  and  using  the  same  principle 
as  the  Pitot  Tube,  the  Orifice  Meter  was  invented  in  the  fall 
of  1911,  by  John  G.  Pew  and  H.  C.  Cooper  of  Pittsburgh,  Pa. 

Mr.  Walter  Abbe,  working  under  the  direction  of  the 
above  named  parties,  spent  approximately  six  months  con- 
ducting experiments  at  the  Wilkinsburg  Test  Station  of  the 
Peoples  Natural  Gas  Co.  It  was  soon  discovered  that  the 
theoretical  formula  worked  out  for  the  principle  of  the  Pitot 
Tube,  would  apply  for  an  Orifice,  so  that  it  was  then  mainly 
a  matter  of  experiment  to  determine  the  shape  of  Orifice  and 
the  manner  of  making  the  connections,  which  would  give  the 
most  consistent  results  and  smallest  variations  between  the 
high  and  low  runs.  These  tests  were  completed  in  Novem- 
ber 1911,  and  the  first  Orifice  meter  for  measuring  gas  was 
installed  on  the  lines  of  the  Hope  Natural  Gas  Company, 
in  West  Virginia. 

The  above  tests  were  made  at  the  reducing  station  of  the 
Peoples  Natural  Gas  Co.,  where  its  main  lines  entering  the 
city  of  Pittsburgh  were  brought  into  one  station  and  from 
which  point  the  gas  was  distributed  at  lower  pressures  to  the 
various  lines  feeding  the  city.  It  can  thus  be  seen  that  these 
tests  were  run  under  actual  working  conditions  at  a  point 
where  any  desired  pressure  from  forty  to  one  hundred  and 
sixty  pounds  could  be  secured,  and  any  volume  up  to  fifty 
million  feet  a  day  was  available  for  the  tests. 

From  that  time  on  the  Orifice  meter  gradually  came  into 
prominence,  though  there  were  other  gas  companies  who  dif- 
fered with  the  Peoples  Natural  Gas  Co.,  as  to  the  thickness  of 
the  Orifice  discs  and  the  manner  of  making  connections. 

*  By  J.  H.  Satterwhite 

11 


GENERAL 


They  decided  to  run  their  own  experiments.  One  of  the  first 
of  these  was  the  United  Natural  Gas  Co.,  of  Oil  City,  Pa. 
Mr.  Thomas  Weymouth,  of  this  company,  conducted  a  large 
number  of  experiments  and  finally  decided  on  the  same  con- 
nections as  used  by  Messrs.  Cooper  and  Pew,  but  used  a 
thinner  disc  with  a  straight  edge,  instead  of  the  beveled 
edge  as  originally  used.  Mr.  Weymouth  finished  his  experi- 
ments in  the  spring  of  1913,  and  later  tests  and  experiments 
have  proven  that  his  formulae  and  coefficients  are  correct. 

The  next  company  to  make  their  own  tests  relative  to 
coefficients,  was  the  Wichita  Pipe  Line  Co.,  now  the  Empire 
Gas  &  Fuel  Co.  Their  first  tests  were  made  at  Joplin,  Mo., 
where  they  had  an  old  artificial  gas  holder  to  use  as  a  standard 
basis  of  measurement.  A  very  interesting  article  covering 
these  tests  and  subsequent  tests  made  at  Wann,  Okla.,  is  to 
be  found  in  the  files  of  the  American  Society  of  Mechanical 
Engineers,  December  1915,  under  the  title  of  "The  Flow  of 
Air  Through  Thin  Plate  Orifices,"  by  E.  O.  Hickstein.  See 
Pages  78  to  98. 

These  tests  were  started  in  August  1913,  and  completed 
in  the  spring  of  1914.  The  Empire  Gas  &  Fuel  Co.,  differed 
slightly  from  the  methods  adopted  by  the  Peoples  Natural 
Gas  Co.,  in  that  although  they  adopted  the  beveled  edge  disc, 
they  also  adopted  the  connections,  now  used  extensively 
throughout  the  Mid-Continent  field, of  2^  times  thediameter 
of  the  pipe  on  the  inlet  side  of  the  Orifice  disc,  and  8  times 
the  diameter  of  the  pipe  on  the  outlet  or  downstream  side 
of  the  Orifice  disc.  Subsequent  tests  at  Erie,  Penna.,  and 
at  several  places  throughout  the  Mid-Continent  field  have 
proven  conclusively  that  the  coefficients  adopted  for  this 
method  of  connection  are  absolutely  correct. 

There  have  been  during  the  past  four  years,  quite  a  few 
tests  that  really  have  no  official  standing  other  than  that 
they  were  check  tests,  all  of  which  have  proven  that  the 
original  work  along  these  lines  was  correct,  and  that  it  is  now 

12 


GENERAL 


optional  to  the  user  as  to  whether  he  desires  to  use  flange 
connection  Orifice  meters,  or  meters  that  use  what  is  called 
full  flow  (2^2  and  8  times  the  diameter)  connections.  The 
main  tihing  to  be  remembered  is,  that  when  using  the  full 
flow  connections  the  static  pressure  must  be  taken  from  the 
upstream  side  of  the  Orifice,  while  for  flange  connections  it  is 
taken  from  the  downstream  side. 

Differential  Gauges — After  the  Peoples  Natural  Gas  Co. 
had  completed  their  original  tests  and  determined  the  ac- 
curacy and  adaptability  of  the  Orifice  meter,  it  was  found 
necessary  to  develop  a  gauge  that  would  record  the  differ- 
ential or  drop  in  pressure  from  one  side  of  the  Orifice  disc 
to  the  other.  It  is  this  development  of  the  recording 
differential  gauge  that  forms  one  of  the  most  interesting 
and  important  stages  of  Orifice  meter  development  of  later 
years. 

At  the  time  when  the  original  experiments  covering  co- 
efficients were  completed  there  was  no  instrument  on  the 
market  for  recording  differential  pressure.  It  was  found 
however,  that  one  of  the  gauge  manufacturers  did  make  a 
recording  gauge  that  recorded  pressure  in  terms  of  inches 
of  water.  On  the  night  of  November  5th,  1911,  at  a  private 
residence  in  Pittsburgh,  a  meeting  of  several  young  men 
interested  in  this  work  was  held.  At  this  meeting  the 
encased  type  differential  gauge,  commonly  called  the  "Bomb 
Shell"  was  developed.  This  consisted  of  a  skeleton  con- 
structed common  recording  pressure  gauge,  with  chart 
graduated  in  inches  of  water  pressure,  encased  within  a  heavy 
casting.  This  casting  was  slightly  larger  than  the  recording 
gauge  and  made  to  stand  a  high  pressure.  It  had  a  cover 
bolted  on,  and  through  the  cover  were  two  peep  holes,  through 
which  one  could  watch  the  action  of  the  gauge  within.  From 
the  spring  a  line  leading  through  the  casting  was  connected 
to  the  high  or  upstream  side  of  the  Orifice,  which  permitted 
the  higher  pressure  to  be  exerted  on  the  inside  of  the  spring. 

13 


GENERAL 


From  the  low  or  downstream  side  of  the  Orifice  another  line 
was  connected  to  the  casting,  filling  same  with  gas,  so  that 
the  lower  pressure  was  exerted  on  the  outside  of  the  spring. 
The  spring  would  then  record  the  difference  between  the  two 
pressures,  which  was  the  differential  drop  in  pressure  across 
the  Orifice  disc. 

This  was  rather  a  crude  differential  gauge,  and  its  weight 
made  it  quite  a  cumbersome  affair.  It  was  however,  the 
best  that  could  be  secured  in  the  short  time  allowed,  and 
afterwards  proved  to  be  the  best  gauge  of  its  type,  until  the 
mercury  float  type  differential  gauge  was  developed  in  later 
years.  There  are  still  a  large  number  of  "Bomb  Shells"  in 
operation  in  West  Virginia  and  Pennsylvania,  and  outside 
of  the  fact  that  the  springs  have  to  be  replaced  frequently, 
they  are  giving  very  good  satisfaction. 

The  gauge  manufacturers  immediately  took  up  the  work 
of  designing  a  differential  gauge  that  would  give  satisfactory 
service  and  eliminate  the  objectionable  features  of  the  "Bomb 
Shell."  They  turned  out  during  the  next  few  years  quite  a 
few  types  of  differential  gauge,  using  springs,  but  they  all 
had  the  same  trouble  as  the  "Bomb  Shell,"  namely  that  it 
took  too  many  springs  to  keep  them  in  operation  and  they 
were  not  sensitive  enough. 

The  Bristol  Co.,  of  Waterbury,  Conn.,  was  the  first  of  the 
gauge  manufacturers  to  get  out  a  mercury  float  type  differ- 
ential gauge,  and  there  are  a  few  of  these  that  are  now  obsolete 
in  the  fields.  This  gauge  never  gave  satisfaction,  as  it  could 
not  be  kept  adjusted,  and  besides  was  constantly  losing  mer- 
cury. Under  these  conditions  it  was  not  as  good  as  the 
spiring  type.  However,  they  had  the  right  idea,  as  has  been 
proven,  namely  using  a  mercury  seal  instead  of  a  spring, 
and  it  never  has  been  thoroughly  understood  why  their 
engineers  dropped  the  gauge  at  this  point  and  did  not  perfect 
it,  unless  as  has  been  stated,  they  did  not  desire  to  go  into 
the  Orifice  meter  business. 

14 


GENERAL 


Fig.  8— "BOMBSHELL"  TYPE  DIFFERENTIAL  GAUGE.    COVER 
REMOVED.      NOTE  LARGE  PIPE  DEADENERS  IN 
GAUGE  LINES 


15 


GENERAL 


Fig.  9— ANOTHER  VIEW  OF  "BOMBSHELL"  TYPE  GAUGE 


16 


GENERAL 


Natural  Gas  Companies   Develop   Proper   Gauge — The 

gas  companies  realized  the  importance  of  a  high  class 
differential  gauge  and  from  two  entirely  different  sources 
plans  were  started  to  develop  a  mercury  float  type  differ- 
ential gauge;  one  in  the  Mid-Continent  fields,  and  the 
other  in  the  Ohio  fields.  From  their  investigations  and 
plans  were  developed  the  two  differential  gauges  that  are  on 
the  market  today.  Both  of  these  gauges  have  undergone  a 
large  number  of  improvements  since  their  invention  in  1914 
and  who  can  say  that  there  are  not  a  large  number  of  im- 
provements still  to  come. 

Adaptability  of  Orifice  Meter — The  Orifice  meter  is  now 
used  for  the  measurement  of  coke  oven  gas,  manufactured 
gas  of  all  kinds,  steam,  water  and  oil. 

It  will  be  seen  from  the  above  that  the  adaptability  of 
this  type  of  meter  for  the  measurement  of  both  gases  and 
liquids  is  practically  unlimited. 

These  different  uses  for  which  the  Orifice  meter  is  adapted 
simplifies  the  work  of  the  purchasing  agent*  especially  the 
purchasing  agent  who  would  have  to  contend  with  the  pur- 
chasing of  meters  for  both  gases  and  liquids.  By  adopting 
the  Orifice  meter,  all  he  has  to  do  is  to  watch  his  warehouse 
stock  and  keep  same  replenished.  If  an  engineer  desires  a 
meter  to  measure  gas,  he  can  go  to  the  warehouse  and  secure 
one.  If  another  man  desires  a  meter  to  measure  oil  he  can 
go  to  the  warehouse  and  secure  the  same  kind  of  me,ter,  which 
also  applies  to  the  man  who  desires  to  measure  steam. 
Different  coefficients  are  applied,  according  to  the  gas  or 
liquid  which  they  desire  to  measure,  but  the  apparatus  is 
the  same. 

It  is  not  altogether  the  desire  for  a  meter  which  will  give 
them  correct  measurement  that  has  caused  so  many  engineers 
to  adopt  the  Orifice  meter,  but  there  is  another  factor  entering 
into  its  use  that  has  strongly  appealed  to  them.  That  is — 
the  Orifice  meter  will  tell  them  to  a  large  extent  exactly 

17 


GENERAL 


what  is  taking  place  in  the  lines  or  at  their  plants.  For 
instance,  the  meter  measuring  oil  at  a  refinery,  not  only  tells 
the  engineers  how  much  oil  has  been  used  during  the  past 
twenty-four  hours,  but  also  tells  them  the  rate  per  hour,  also 
whether  their  pumper  has  been  keeping  his  pumps  going  at  a 
uniform  rate  of  speed,  or  whether  he  pumps  too  much  one 
hour  and  not  enough  another  hour.  It  helps  them  greatly 
in  smoothing  out  their  operations,  so  that  they  can  secure 
greater  efficiency  and  better  products  at  a  uniform  rate  of 
operation.  The  same  idea  applies  when  measuring  steam, 
as  the  engineer  then  knows  exactly  how  to  handle  his  boiler 
room  under  different  and  varying  loads,  and  knows  how 
these  loads  are  pro-rated  throughout  the  plant. 

Likewise,  in  the  gas  business  it  tells  its  own  story,  in  that 
»the  superintendent  will  know  whether  his  field  men  are 
drawing  on  his  wells  at  a  uniform  rate  of  flow  or  whether  they 
pull  on  one  well  hard  for  a  while,  and  then  ease  up  and 
draw  on  another  one  heavy  for  a  while.  This  is  especially 
desirous  at  this  time,  when  so  many  of  the  states  in  the  Mid- 
dle West  have  passed  laws  regulating  the  percentage  of  the 
open  flow  of  a  gas  well  that  may  be  taken  in  twenty-four 
hours.  It  likewise  helps  the  town  superintendent  in  pro- 
viding daily  records  enabling  him  to  properly  take  care  of 
his  varying  loads.  The  pipe  line  superintendent  can  also 
tell  whether  his  men  are  taking  proper  care  of  the  drips  along 
the  line,  because  a  heavy  accumulation  of  gasoline  conden- 
sate  or  water  in  the  lines  would  be  shown  on  the  Orifice  meter 
chart  by  a  vibration  of  the  differential  pen  arm.  It  can 
thus  be  seen  that  not  only  does  the  Orifice  meter  measure 
accurately  the  liquid  or  gas  passing  through  the  pipe  line,  but 
also  gives  its  owner  a  definite  record  of  what  is  transpiring 
relative  to  various  operations." 


18 


PART   TWO 

PHYSICAL  PROPERTIES  OF  FLUIDS 


The  flow  of  fluids  follows  the  physical  laws  which  were 
discovered  centuries  ago.  These  laws  and  the  properties  of 
fluids  which  are  the  basis  of  the  derivation  oi:  the  simple 
formula  for  the  flow  through  an  Orifice  are  explained  in  de- 
tail in  the  following  pages.  No  attempt  is  made  to  explain 
the  problems  of  thermodynamics,  pneumatics,  etc.,  but 
only  to  give  an  outline  of  those  laws  leading  up  to  the  formula 
universally  used. 

Theory  of  the  Constitution  of  Matter — Physicists  have 
generally  adopted  the  following  theory  of  the  constitution 
of  matter.  Every  body  of  matter  is  composed  of  exceedingly 
small  particles,  called  molecules,  in  other  words,  every  body 
is  the  sum  of  its  molecules.  No  two  molecules  of  matter  in 
the  universe  are  in  contact  with  each  other.  Every  molecule 
of  a  body  is  separated  from  its  neighbors,  on  all  sides,  by 
inconceivably  small  spaces.  Every  molecule  is  in  quivering 
motion  in  its  little  space,  moving  back  and  forth  between 
its  neighbors,  and  rebounding  from  them.  When  we  heat  a 
body  we  simply  cause  the  molecules  to  move  more  rapidly 
through  their  spaces;  so  they  strike  harder  blows  on  their 
neighbors,  and  usually  push  them  away  a  very  little;  hence, 
the  size  of  the  body  increases.  This  theory  seems,  at  first, 
little  more  than  an  extravagant  guess.  But  it  shall  be 
found  that  this  theory  enables  us  to  account  for  most  of  the 
known  phenomena  of  matter. 

States  of  Matter — For  the  purposes  of  subdivision  we 
may  say  that  matter  exists  in  three  distinct  states,  the  solid, 
the  liquid,  and  the  gaseous.  In  addition,  however,  to  states 

19 


PHYSICAL    PROPERTIES     OF    FLUIDS 

which  fulfill  the  definitions  of  a  solid,  a  liquid,  or  a  gas,  which 
we  shall  give  later  on,  it  will  be  found  that  there  are  inter- 
mediate states  which  bridge  over  the  intervals  between  the 
solid  and  the  liquid,  and  the  liquid  and  the  gas.  As  an  ex- 
ample of  the  kind  of  gradation  which  exists,  we  may  take  the 
following:  steel,  lead,  wax,  cobbler's  wax  (which  will  flow 
like  a  liquid  if  allowed  sufficient  time),  water,  ether,  steam, 
air,  hydrogen.  In  addition  there  is  the  critical  state  when 
a  substance  is  to  all  intents  and  purposes  both  a  liquid  and  a 
gas. 

We  may  define  a  solid  as  a  portion  of  matter  which  is 
able  to  support  a  steady  longitudinal  stress  without  lateral 
support.  In  contradistinction,  a  portion  of  matter  which  is 
unable  to  support  a  steady  longitudinal  stress  without  lateral 
support  is  called  a  fluid. 

If  we  take  a  solid  body,  say  a  lead  pencil,  then  we  may 
apply  a  deforming  force,  either  of  compression  or  extension, 
in  any  direction  to  the  pencil,  and  there  will  be  a  certain 
amount  of  strain,  either  elongation,  compression,  or  bending 
produced,  which  will  call  into  play  a  stress  that  will  be  in 
balance  with  this  force,  and  this  stress  will  be  produced 
without  the  body  being  supported  in  any  way  in  a  direction 
at  right  angles  to  that  along  which  the  stress  acts.  In  the 
case  of  a  fluid,  such  as  water  or  air,  we  are  unable  to  exert  a 
stress  on  it,  and  hence  produce  a  corresponding  strain,  unless 
we  supply  some  constraining  boundary  which  shall  prevent 
the  fluid  swelling  out  at  right  angles  to  the  line  of  action  of 
the  stress. 

Fluids,  Liquids  and  Gases — Fluids  are  divided  into 
liquids  and  gases.  A  liquid  is  a  fluid  such  that  when  a  certain 
volume  is  introduced  into  a  vessel  of  greater  volume  it  only 
occupies  a  portion  of  the  vessel  equal  to  its  own  volume. 
A  gas  is  a  fluid  such  that  if  a  certain  volume  is  introduced  into 
a  vessel,  then,  whatever  the  volume  of  the  vessel  may  be, 
the  gas  will  distribute  itself  throughout  the  vessel. 

•      20 


PHYSICAL    PROPERTIES     OF    FLUIDS 


Vapor — Vapor  is  essentially  the  same  as  gas,  but  the 
word  vapor  is  conveniently  limited  to  the  gaseous  state  of  a 
body  which  is  liquid  or  solid  at  ordinary  temperatures,  while 
the  term  "gas"  is  applied  to  those  fluids  which  are  in  that 
rarified  state  at  ordinary  temperatures. 

Vapor  and  Gas — A  vapor  is  a  substance  in  the  gaseous 
state  at  any  temperature  below  the  critical  point.  A  vapor 
can  be  reduced  to  a  liquid  by  pressure  alone,  and  may  exist 
as  a  saturated  vapor  in  the  presence  of  its  own  liquid.  A 
gas  is  the  form  which  any  liquid  assumes  above  its  critical 
temperature,  and  it  cannot  be  liquefied  by  pressure  alone, 
but  only  by  combined  pressure  and  cooling.  The  critical 
point  is  the  lowest  temperature  of  a  gas  at  which  it  cannot 
be  liquefied  by  pressure.  The  critical  point  is  the  line  of 
demarcation  between  a  vapor  and  a  gas.  The  temperature  of 
the  substance  at  the  critical  point  is  the  critical  temperature. 
The  pressure  which  at  the  critical  temperature  just  suffices 
to  condense  the  gas  to  the  liquid  form  is  called  the  critical 
pressure. 

Table  1 

CRITICAL  TEMPERATURES  AND  PRESSURES 
OF  VARIOUS  GASES 


Chemical 

Critical 

Critical 

Gases  or  Vapors 

Formula 

Temp.  deg. 

Pressure,  Ib. 

fahr. 

per  sq.  in.  abs. 

Water 

H20 

689 

2940 

Ammonia 

NH3 

266 

1691 

Acetylene 

C2H2 

99 

Carbon  Dioxide 

C02 

88 

1103 

Ethylene 

C2H4 

50 

760 

Methane 

CH4 

-115 

807 

Oxygen 

02 

-182 

747 

Argon 

A2 

-186 

744 

Carbon  Monoxide 

CO 

-219 

522 

Air 

-220 

573 

Nitrogen 

N2 

-231 

515 

Hydrogen 

H2 

-389 

294 

21 


PHYSICAL    PROPERTIES     OF    FLUIDS 

Gravitation — That  attraction  which  is  exerted  on  all 
matter,  at  all  distances,  is  called  gravitation.  Gravitation 
is  universal,  that  is,  every  molecule  of  matter  attracts  every 
other  molecule  of  matter  in  the  universe.  The  whole  force 
with  which  two  bodies  attract  one  another  is  the  sum  of  the 
attractions  of  their  molecules,  and  depends  upon  the  number 
of  molecules  the  two  bodies  collectively  contain,  the  mass  of 
each  molecule,  and  the  distance  between  the  bodies.  What 
is  understood  by  the  weight  of  a  body  is  the  mutual  attraction 
between  it  and  the  earth. 

The  force  of  gravity  varies  with  the  distance  from  the 
center.  Observations  made  in  various  ways  show  that  the 
force  of  gravity  varies  over  the  surface  of  the  earth.  Now  it 
is  found  that  the  nearer  an  object  without  the  earth's  sur- 
face is  to  the  center  of  the  earth,  the  greater  is  the  force  of 
gravity.  The  polar  diameter  of  the  earth  is  about  26  miles 
less  than  its  equatorial  diameter,  and  consequently,  the  dis- 
tance from  the  center  to  the  surface  at  the  poles  is  13  miles 
less  than  to  the  surface  at  the  equator.  This  considerable 
difference  in  distance  from  the  center  occasions  an  appreci- 
able difference  between  the  weight  of  a  body  (having  any 
considerable  mass)  at  the  equator  and  at  the  poles;  and,  since 
the  distance  of  the  surface  from  the  center  constantly  in- 
creases as  we  go  from  the  poles  toward  the  equator,  the  weight 
of  all  objects  transported  from  the  poles  toward  the  equator 
constantly  diminishes. 

Fluid  Pressure — With  the  exception  of  the  phenomena 
of  capillarity  and  those  occasioned  by  difference  in  compres- 
sibility and  expansibility,  liquids  and  gases  are  governed  by 
the  same  laws. 

We  are  placed  on  the  borders  of  two  oceans.  A  watery 
ocean  borders  our  land;  an  aerial  ocean,  which  is  called  the 
atmosphere,  surrounds  us.  Every  molecule,  in  both  the 
gaseous  and  liquid  oceans,  is  drawn  toward  the  earth's  center 

22 


PHYSICAL     PROPERTIES     OF    FLUIDS 


PHYSICAL    PROPERTIES     OF    FLUIDS 


Fig.  11— ORIFICE  METER  ON  LARGE    GAS    MAIN 


PHYSICAL     PROPERTIES     OF    FLUIDS 

by  gravity.     This  gives  to  both  fluids  a  downward  pressure 
upon  everything  upon  which  they  rest. 

The  gravitating  power  of  liquids  is  everywhere  apparent, 
as  in  the  fall  of  drops  of  rain,  the  descent  of  mountain  streams, 
the  power  of  falling  water  to  propel  machinery,  and  the 
weight  of  water  in  a  bucket.  The  downward  pressure  of  air 
is  indicated  by  a  barometer. 

Compressibility  and  Expansibility  of  Gases — The  in- 
crease of  pressure  attending  the  increase  in  depth,  in  both 
liquids  and  gases,  is  readily  explained  by  the  fact  that  the 
lower  layers  of  fluids  sustain  the  weight  of  all  the  layers 
above.  Consequently,  if  the  body  of  fluid  is  of  uniform 
density,  as  is  very  nearly  the  case  in  liquids,  the  pressure  will 
increase  in  nearly  the  same  ratio  as  the  depth  increases. 
But  the  aerial  ocean  is  far  from  being  of  uniform  density, 
in  consequence  of  the  extreme  compressibility  of  gaseous 
matter.  The  contrast  between  water  and  air,  in  this  respect, 
may  be  seen  in  the  fact  that  water,  subjected  to  a  pressure  of 
one  atmosphere,  contracts  .0000457  of  its  volume;  under 
the  same  circumstances,  air  contracts  one-half.  For  most 
practical  purposes,  we  may  regard  the  density  of  water  at  all 
depths  as  uniform,  while  it  is  far  otherwise  in  large  masses 
of  gases. 

The  pressure  at  different  depths  in  liquids  may  be  illus- 
trated by  piling  several  bricks  one  on  another,  when  the 
pressure  that  different  bricks  sustain  varies  directly  with 
their  depths  below  the  upper  surface  of  the  pile.  On  the 
other  hand,  pressure  of  gases  at  different  depths  may  be 
illustrated  by  piling  fleeces  of  wool  one  on  another.  Since 
the  volume  of  each  successive  fleece  varies  with  the  weight 
it  bears,  the  pressure  which  different  fleeces  sustain  are  not 
proportional  to  their  respective  depths  below  the  upper 
surface  of  the  pile.  At  twice  the  depth,  there  would  be 
much  more  than  twice  the  pressure,  because  the  lower  point 
would  sustain  more  than  twice  the  number  of  fleeces. 

25 


PHYSICAL    PROPERTIES     OF    FLUIDS 

Closely  allied  to  compressibility  is  the  elasticity  of  gases, 
or  their  power  to  recover  their  former  volume  after  com- 
pression. The  elasticity  of  all  fluids  is  perfect.  By  this  is 
meant,  that  the  force  exerted  in  expansion  is  always  equal 
to  the  force  used  in  compression;  and  that,  however  much  a 
fluid  is  compressed,  it  will  always  completely  regain  its 
former  bulk  when  the  pressure  is  removed.  Liquids  are 
perfectly  elastic;  but,  inasmuch  as  they  are  perceptibly 
compressed  only  under  tremendous  pressure,  they  are  re- 
garded as  practically  incompressible  and  so  it  is  rarely 
necessary  to  consider  their  elasticity.  It  has  already  been 
stated  that  matter  in  a  gaseous  state  expands  indefinitely, 
unless  restrained  by  external  force.  The  atmosphere  is 
confined  to  the  earth  by  the  force  of  gravity. 

Expansive  Power  of  Gases — The  property  of  gases  which 
distinguishes  them  from  other  fluids  is  that  a  given  mass  of 
gas,  when  introduced  into  a  closed  vessel,  always  exactly 
fills  the  vessel,  whatever  its  volume.  Thus  if  we  have  two 
equal  closed  vessels  connected  together  by  a  tube  which  can 
be  closed  by  means  of  a  tap,  and  one  of  these  vessels  is  filled 
with  a  gas,  say  air  at  the  ordinary  pressure,  while  the  other 
does  not  contain  any  matter,  or,  in  other  words,  has  a  vacuum 
inside,  then,  on  opening  the  tap,  the  air  immediately  expands 
and  rushes  into  the  second  vessel,  till  finally  there  is  the  same 
quantity  of  gas  in  each  vessel.  By  again  closing  the  tap 
and  exhausting  the  air  from  one  of  the  vessels  by  means  of 
an  air  pump,  and  then  opening  the  tap,  the  remaining  gas 
again  expands  and  fills  the  two  vessels.  This  operation 
may  be  repeated  indefinitely,  and  in  every  case  the  gas  left 
in  the  one  vessel  will,  when  the  tap  is  opened,  expand  and  fill 
the  two  vessels.  This  experiment  illustrates  the  expansive 
power  of  gases. 

Since  the  gas  enclosed  in  a  vessel  always  expands  and 
completely  fills  the  vessel,  even  if  this  latter  is  increased  in 
volume,  it  follows  that  the  gas  must  exert  a  pressure  on  the 

26 


PHYSICAL    PROPERTIES     OF    FLUIDS 

inside  of  the  containing  vessel.  That  this  is  so  can  be  shown 
by  enclosing  some  air  at  ordinary  atmospheric  pressure  in  a 
thin  glass  flask,  and  then  removing  the  air  from  outside 
the  flask  by  placing  it  beneath  the  receiver  of  an  air  pump, 
when,  unless  the  flask  is  fairly  strong,  the  pressure  exerted 
by  the  air  inside  the  flask  will  be  sufficient  to  burst  the  flask. 
The  reason  that  the  flask  does  not  burst  before  the  air 
surrounding  it  is  removed,  is  that  the  air  surrounding  the 
flask  presses  on  the  outside  of  the  flask  and  counteracts  the 
effect  of  the  pressure  of  the  enclosed  air  on  the  inside.  When 
the  air  outside  is  removed  by  means  of  the  pump  there  is  no 
pressure  exerted  on  the  outside,  and  the  flask  may  not  be 
strong  enough  to  withstand  the  inside  pressure. 

Pascal's  Law — An  exterior  pressure  applied  to  a  fluid  is 
transmitted  equally  in  all  directions,  or  the  pressure  per  unit 
of  area  exercised  inward  upon  a  mass  of  fluid  is  transmitted 
undiminished  in  all  directions,  and  acts  with  the  same  force 
upon  all  surfaces  in  a  direction  at  right  angles  to  those  sur- 
faces. Hence,  the  pressure  applied  to  any  area  of  a  confined 
fluid  is  transmitted  to  every  other  equal  area  through  all 


Fig.  12— DIAGRAM  ILLUSTRATING  PASCAL'S  LAW 

the  fluid  to  the  walls  of  the  containing  chamber  without 
diminution,  as  shown  in  the  diagram  above.  According  to 
this  law,  the  gas  pressures  in  the  various  parts  of  a  "contin- 
uous and  connected  reservoir"  must  be  equal.  The  total 
pressure  acting  upon  any  definite  portion  of  the  surface  is 

27 


PHYSICAL    PROPERTIES     OF    FLUIDS 


equal  to  the  pressure  exerted  by  the  head  of  fluid  itself 
plus  the  effect  of  the  exterior  pressure,  which  is  transmitted 
by  the  fluid. 

PRESSURE  AND  LIQUID  HEAD 


F         4 

1 

K                     L\ 

.   =™^x?^>i 

L^r^l^l  :! 

:  =  =  =  ^-=--  S  -'--3 

r^  

A                  B 

C                  D 

m  f",  m 

•  5"  • 

1 

£ 

/• 

-I? 


Fig.  13  Fig.  14 

The  fact  that  the  pressure  of  a  liquid  depends  only  upon 
the  head  may  be  illustrated  by  the  above  diagrams.  As- 
suming the  above  vessels  as  one  inch  wide  and  filled  with 
water  to  the  elevations  indicated,  the  total  pressure  acting 
on  the  surface  A  to  D  is  48  cubic  inches  of  water  or  4  cubic 
inches  of  water  on  each  square  inch.  Since  BC  is  2  inches 
the  total  pressure  acting  on  BC  is  2X4  or  8  cubic  inches. 
The  total  pressure  acting  on  EF  is  equal  to  the  pressure  at 
BC  plus  the  weight  of  the  column  of  water  BE.  Column 
BEFC  contains  32  cubic  inches.  Therefore  the  total  pressure 
on  EF  equals  32+8  or  40  cubic  inches.  Since  EF  is  2  square 
inches  in  area,  the  pressure  per  square  inch  is  20  cubic  inches 
of  water,  or  a  pressure  equal  to  20  inches  head  of  water  which 
is  the  height  of  the  surface  above  EF. 

28 


PHYSICAL    PROPERTIES     OF    FLUIDS 

In  Fig.  14  the  pressure  acting  on  RS  is  16  inches  head  of 
water.  Since  this  pressure  is  transmitted  equally  in  all 
directions  the  pressure  acting  on  each  square  inch  from  Q  to 
T  is  also  equal  to  the  weight  of  16  cubic  inches  of  water.  If 
this  fact  is  not  true  and  the  pressure  near  T  is  less  than  at  S 
then  the  water  would  flow  from  S  toward  T.  Since  these 
points  are  on  the  same  level  and  the  water  is  not  in  motion 
the  pressure  at  each  point  must  be  equal  to  the  pressure  at 
the  other  point.  This  pressure  acts  upward  on  the  container 
from  Q  to  R  from  S  to  T  as  well  as  downward  on  the  liquid 
at  this  level.  Therefore  the  total  pressure  from  Q  to  T  is 
16X12  or  a  weight  of  192  cubic  inches  of  water.  The  total 
pressure  on  surface  OP  is  equal  to  the  pressure  at  QT  plus 
the  weight  of  the  water  between  QT  and  OP  as  the  sides  QO 
and  TP  are  vertical.  This  latter  volume  equals  4X12  or 
48  cubic  inches.  Therefore  the  total  pressure  on  OP  equals 
48+192  or  240  cubic  inches  of  water  on  12  square  inches  of 
surface  or  weight  of  20  cubic  inches  of  water  per  square  inch. 
The  pressure  acting  on  this  surface  is  20  inches  of  water  head. 
Therefore,  liquid  pressure  depends  only  on  the  head  of  liquid 
and  density  and  not  on  total  area.  The  expression  "feet 
head  of  liquid"  is  equivalent  to  a  pressure  per  inch  equal  to 
the  weight  of  a  column  of  liquid;  one  square  inch  in  area 
of  a  height  equal  to  the  feet  head.  If  gasoline  is  used  as  a 
liquid  the  head  in  inches  of  gasoline  on  each  area  would  be 
the  same  as  for  water  but  the  pressure  per  square  inch  would 
be  less  depending  on  the  relative  densities  of  gasoline  and 
water. 

We  conclude,  therefore,  that  the  total  pressure  on  the 
bottom  of  a  vessel  depends  on  the  depth,  the  area  of  the 
bottom,  and  the  density  of  the  liquid,  and  is  independent  of 
the  shape  of  the  vessel  and  the  quantity  of  liquid.  The 
important  fact  that  the  pressure  on  the  bottom  does  not 
depend  on  the  shape  of  the  vessel  is  often  called  the  hydro- 
static paradox,  because  though  true,  it  seems  at  first  absurd. 

29 


PHYSICAL    PROPERTIES     OF    FLUIDS 

The  pressure  due  to  gravity  on  any  portion  of  the  bottom 
of  a  vessel  is  equal  to  the  weight  of  a  column  of  that  liquid 
whose  base  is  the  area  of  that  portion  of  the  bottom  pressed 
upon,  and  whose  height  is  the  greatest  depth  of  the  liquid  in 
the  vessel. 

Evidently  the  lateral  pressure  at  any  point  of  the  side  of 
a  vessel  depends  upon  the  depth  of  that  point;  and,  as  depth 
at  different  points  of  a  side  varies,  hence,  to  find  the  pressure 
upon  any  portion  of  a  side  of  a  vessel,  we  find  the  weight  of 
a  column  of  water  whose  base  is  the  area  of  that  portion  of 
the  side,  and  whose  height  is  the  average  depth  of  that  por- 
tion. Thus,  we  compute  the  total  pressure  on  the  side  UVRS 
of  the  vessel  (Fig.  14),  by  multiplying  the  area  of  the  side 
32  square  inches  (dimensions,  16X2  inches),  by  the  depth  to 
the  middle  point,  8  inches.  The  total  pressure  is  equal  to 
the  weight  of  256  cubic  inches  of  water. 

From  the  preceding  paragraphs  it  is  evident  that  the 
head  of  fluid  acting  on  a  surface  may  be  expressed  in  terms 
of  head  of  any  other  fluid  or  in  terms  of  pressure  per  square 
inch,  also  that  the  pressure  per  square  inch  may  be  expressed 
in  terms  of  liquid  head. 

Since  the  weight  of  water  is  62.355  pounds  per  cubic  foot, 
a  column  of  water  one  foot  high  and  one  square  foot  in  area 
exerts  a  pressure  of  62.355  pounds  on  the  square  foot  of  sur- 
face, 62.3551b.  per  square  foot,  or  0.43302  pounds  per  square 
inch.  Therefore,  a  column  of  water  one  foot  high  and  one 
square  inch  in  area  is  equivalent  to  a  pressure  of  .43302  pounds 
per  square  inch,  and  one  pound  per  square  inch  equals 
2.3094  feet  water  head,  or  one  pound  per  square  inch  equals 
27,71  inches  of  water.  One  inch  of  water  head  exerts  pressure 
of  .03609  pounds  per  square  inch.  Since  the  average  at- 
mospheric pressure  of  the  gas  fields  is  14.4  pounds  per  square 
inch, it  maybe  expressed  asequal  to  (14.4X2,3094)  or 33.3 feet 
water  head.  It  also  may  be  expressed  as  399  (14.4X27.71  = 
399)  inches  water  head.  In  the  same  manner  one  inch  of 

30 


PHYSICAL    PROPERTIES     OF    FLUIDS 


Table  2— PRESSURE  EQUIVALENTS 


Ounces 

In. 
Water 

In. 

Mer- 
cury 

In. 
Mer. 
cury 

Ounces 

In. 
Water 

In. 
Water 

In. 
Mer- 
cury 

Ounces 

.25 

.43 

.032 

1. 

7.85 

13.60 

.25 

.018 

.144 

.50 

.87 

.064 

1.5 

11.78 

20.40 

.50 

.037 

.259 

.75 

1.30 

.095 

2. 

15.71 

27.20 

.75 

.055 

.433 

1. 

1.73 

.127 

2.5 

1.23  Ib. 

34.00 

1. 

.074 

.577 

2. 

3.46 

.26 

3. 

1.47    " 

40.80 

2. 

.147 

1.15 

3. 

5.19 

.38 

3.5 

1.72    " 

47.60 

3. 

.22 

1.73 

4. 

6.92 

.51 

4. 

1.96    " 

54.40 

4. 

.29 

2.31 

5. 

8.65 

.64 

4.5 

2.21     " 

61.20 

5. 

.37 

2.89 

6. 

10.38 

.77 

5. 

2.45    " 

68.00 

6. 

.44 

3.46 

7. 

12.11 

.89 

5.5 

2.74    " 

74.80 

7. 

.51 

4.04 

8. 

13.85 

1.02 

6. 

2.94    " 

81.60 

8. 

.59 

4.62 

9. 

15.58 

1.15 

6.5 

3.19    " 

88.40 

9. 

.66 

5.20 

10. 

17.31 

1.27 

7. 

3.44    " 

95.20 

10. 

.74 

5.77 

11. 

19.05 

1.40 

7.5 

3.68    " 

102.00 

11. 

.81 

6.35 

12. 

20.78 

1.53 

8. 

3.93    " 

108.80 

12. 

.88 

6.93 

13. 

22.51 

1.66 

8.5 

4.17    " 

115.61 

13. 

.96 

7.51 

14. 

24.24 

1.78 

9. 

4.42     " 

122.41 

14. 

1.03 

8.08 

15. 

25.97 

1.91 

9.5 

4.66    " 

129.21 

15. 

1.10 

8.66 

16  or  1  Ib. 

27.71 

2.04 

10. 

4.91    " 

136.01 

16. 

.18 

9.24 

1   Ib.loz. 

29.44 

2.16 

10.5 

5.15    " 

142.81 

17. 

.25 

9.82 

"      2  " 

31.17 

2.29 

11. 

5.40    " 

149.61 

18. 

.32 

10  .  39 

"      3  " 

32.90 

2.42 

11.5 

5  .  64    " 

156.41 

19. 

.40 

10.97 

"      4  " 

34.63 

2.55 

12. 

5  .  89    " 

163.21 

20. 

.47 

11.55 

"      5  " 

36.36 

2.67 

12.5 

6.14    " 

170.01 

21. 

.54 

12.13 

"      6  " 

38.09 

2.80 

13. 

6.38    " 

176.81 

22. 

.62 

12.70 

"      7  " 

39.82 

2.93 

13.5 

6.63    " 

183.61 

23. 

.69 

13.28 

«            g    « 

41.56 

3.06 

14. 

6.87    " 

190.41 

24. 

.76 

13.86 

"      9  " 

43.29 

3.18 

14.5 

7.12    " 

197.21 

25. 

.84 

14.44 

"    10  " 

45.02 

3.31 

15. 

7.36    " 

204.01 

26. 

.91 

15.01 

«    n  « 

46.76 

3.44 

15.5 

7  61    " 

210.81 

27. 

.99 

15.59 

"    12  " 

48.49 

3.57 

16. 

7.85    " 

217.61 

27.71 

2.04 

16  or  1  Ib. 

«    13  « 

50.22 

3.69 

16.5 

8.10    " 

224.41 

29. 

2.13 

1.05    Ib. 

«    14  « 

51.95 

3.82 

17. 

8.34    " 

231.21 

30. 

2.21 

1.08    " 

"    15" 

53  .  68 

3.95 

17.5 

8  .  59    " 

238.01 

31. 

2.28 

1.12    " 

21b. 

55.42 

4.07 

18. 

8.83    " 

244.81 

32. 

2.35 

1.15    " 

2  Ib.  loz. 

57.15 

4.20 

18.5 

9.08    " 

251.61 

33. 

2.43 

1.19    " 

"      2  " 

58.88 

4.33 

19. 

9.33    " 

258.41 

34. 

2.50 

1.23    " 

«      3  « 

60.62 

4.46 

19.5 

9.57    " 

265.21 

35. 

2.57 

1.26    " 

««      4  « 

62.35 

4.59 

20. 

9.82    " 

272.01 

36. 

2.65 

1.30    " 

«      5« 

64.08 

4.71 

20.5 

10.06    " 

278.81 

37. 

2.72 

1.34    " 

«      6  « 

65.81 

4.84 

21. 

10.31    " 

285.61 

38. 

2.79 

1.37     ' 

"      7  " 

67.54 

4.97 

21.5 

10.55    " 

292.41 

39. 

2.87 

1.41 

"      8  " 

69.27 

5.10 

22. 

10.80    " 

299.21 

40. 

2.94 

1.44 

"      9  " 

71.01 

5.22 

22.5 

H.04    " 

306.01 

41. 

3.01 

1.48 

"    10  " 

72.74 

5.35 

23. 

11.29    " 

312.81 

42. 

3.09 

1.52 

"    11  " 

74.47 

5.48 

23.5 

11.53     " 

319.61 

43. 

3.16 

1.55 

"    12  " 

76.20 

5.60 

24. 

11.78    " 

326.41 

44. 

3.24 

1.59 

"    13  " 

77.93 

5.73 

24.5 

12.02    " 

333.21 

45. 

3.31 

1.62 

"    14  " 

79.67 

5.86 

25. 

12.27    " 

340.02 

46. 

3.38 

1.66 

"    15  " 

81.40 

5.99 

25.5 

12.52    " 

346.82 

47. 

3.46 

1.70 

31b. 

83.13 

6.11 

26. 

12.76    " 

353.62 

48. 

3.53 

1.73 

"     loz. 

84.86 

6.24 

26.5 

13.01     " 

360.42 

49. 

3.60 

1.77 

"      2  " 

86.59 

6.37 

27. 

13.25    " 

367  .  22 

50. 

3.68 

1.80 

«      3  « 

88.33 

6.50 

27.5 

13.50    " 

374.02 

51. 

3.75 

1.84 

:         4   « 

90.06 

6.62 

28. 

13.74    " 

380  .  82 

52. 

3.82 

1.88 

«         g  « 

91.79 

6.75 

28.5 

13.99     " 

387.62 

53. 

3.90 

1.91 

"      6  " 

93.52 

6.88 

29. 

14.23     " 

394.42 

54. 

3.97 

1.95 

"     7  " 

95.65 

7.01 

29.5 

14.48    " 

401.22 

55.42 

4.07 

2.  Ib. 

"      8  " 

96.98 

7.13 

30. 

14.7^2    " 

408.02 

31 


PHYSICAL    PROPERTIES     OF    FLUIDS 


mercury  is  equivalent  to  .4908  pounds  per  square  inch  as  one 
cubic  inch  of  mercury    weighs  .4908  pounds.     One  inch  of 

.4908 
mercury  is  equal  to  — 

.03609 


or  13.6  inches  of  water. 


Pressure  Equivalents. 

One  inch  of  mercury  =  .4908  Ib.  per  square  inch. 
One  inch  of  mercury  =  13.6  inches  of  water. 
One  foot  of  water,  62  deg.  fahr.  =  62.355  Ib.  per  square  foot. 
One  foot  of  water,  62  deg.  fahr.  =  .43302  Ib.  per  square  inch. 
One  inch  of  water,  62  deg.  fahr.  =  .03609  Ib.  per  square  inch. 
One  inch  of  water,  62  deg.  fahr.  =  .07353  inches  of  mercury. 
One  pound  per  square  inch  =  2. 0375  inches  of  mercury. 
One  pound  per  square  inch  =  27. 712  inches  of  water. 
One  pound  per  square  inch  =  2. 3094  feet  of  water. 

ATMOSPHERIC  PRESSURE 


-rA 


30' 


Fig.  15 

If  the  closed  end  of  the  U  tube,  (Fig.  15)  having  a  bore 
one  square  inch  in  area,  is  filled  with  mercury,  and  then  in- 
verted ;  the  mercury  in  the  closed  arm  will  sink  to  A,  and  will 
rise  in  the  open  arm  to  C.  At  sea  level  the  surface  A  is  30 
inches  higher  than  the  surface  C.  This  can  be  accounted  for 

32 


PHYSICAL    PROPERTIES     OF    FLUIDS 


only  by  the  atmospheric  pressure.  The  column  of  mercury 
BA,  containing  30  cu.  inches,  is  an  exact  counterpoise  for  a 
column  of  air  of  the  same  area  extending  from  C  to  the  upper 
limit  of  the  atmospheric  ocean,  an  unknown  height. 

The  weight  of  the  30  cu.  inches  of  mercury  in  the  column 
BA  is  14.7  lb.,  which  is  the  weight  of  a  column  of  air  of  one 
square  inch  section,  extending  from  the  surface  of  the  sea  to 
the  upper  limit  of  the  atmosphere.  But  gravity  causes 
equal  pressure  in  all  directions.  At  the  level  of  the  sea,  all 
bodies  are  pressed  upon  in  all  directions  by  the  atmosphere, 
with  a  force  of  about  14.7  lb.  per  square  inch,  over  one  ton 
per  square  foot.  R  egardless  of  the  size  of  the  bore  of  the  tube 
the  pressures  per  square  inch  would  be  the  same,  and  as 
liquid  head  is  independent  of  the  shape  of  the  container,  the 
head  would  be  the  same  for  any  shape  of  tube. 


-30" 


-20' 


-10" 


Y\ 


Fig.  16 

Barometer — Fig.  16  represents  another  form  of  apparatus 
which  is  more  commonly  used  for  ascertaining  atmospheric 
pressure.  It  consists  of  a  straight  glass  tube  about  36  inches 
long,  closed  at  one  end,  and  filled  with  mercury.  When  this 
tube  is  inverted,  the  open  end  having  been  covered  with  a 
finger  and  plunged  into  an  open  cup  of  mercury,  and  the 

33 


PHYSICAL    PROPERTIES     OF    FLUIDS 

finger  withdrawn,  the  mercury  in  the  tube  will  sink  until  it 
balances  the  atmospheric  pressure.  This  experiment  was 
devised  by  Torricelli,  an  Italian.  The  apparatus  is  called  a 
barometer.  The  empty  space  above  the  mercury  in  the 
tube  is  called  a  Torricellian  vacuum.  If  water  is  used  in  a 
very  long  tube  instead  of  mercury  the  height  XY  would  be 
about  34  feet  or  13.6  times  as  high  as  for  mercury  at  sea  level. 

If  the  barometer  is  carried  up  a  mountain,  it  is  found  that 
the  mercury  constantly  falls  as  the  ascent  increases.  This 
shows  that  the  pressure  is  less  near  the  top  of  the  aerial 
ocean  than  near  its  bottom.  It  is  found  that  the  pressure 
increases  very  rapidly  upon  descending  when  near  the  bot- 
tom. 

The  density  of  the  air  at  a  height  of  3  miles  is  but  little 
more  than  y%  the  density  at  the  sea  level;  at  6  miles,  J4;  at  9 
miles,  y%',  at  15  miles,  j^]  at  35  miles  it  is  calculated  to  be 
only  3oooo>  so  that  the  greatest  part  of  the  atmosphere  must 
be  within  that  distance  of  the  surface  of  the  earth.  On  the 
other  hand,  if  an  opening  could  be  made  in  the  earth,  35 
miles  in  depth  below  the  sea.  level,  it  is  calculated  that  the 
density  of  the  air  at  the  bottom  would  be  1,000  times  greater 
than  at  the  sea  level,  so  that  water  would  float  in  it. 

The  average  height  of  mercury  in  the  vacuum  column 
above  the  mercury  varies  with  the  altitude  of  the  places  and 
in  most  of  the  gas  fields  is  about  29.34  inches  which  is  equal 
to  14.4  pounds  per  square  inch  (29.34  X. 4908  =  14.4). 

Absolute  Pressure — If  several  glass  tubes  of  various 
areas,  sealed  at  one  end  are  filled  with  the  mercury,  the 
open  ends  immersed  in  a  deep  bowl  of  mercury  (as  in  Fig.  16) 
and  the  sealed  ends  lifted  above  the  mercury,  the  tubes  will 
remain  filled  with  mercury  until  the  sealed  ends  are  lifted 
to  a  certain  level  above  the  surface  of  the  mercury,  before  a 
vacant  space  will  be  formed,  after  which  any  additional 
elevation  of  the  tubes  will  fail  to  increase  the  height  of  the 
mercury  in  the  tubes  above  the  surface  of  the  mercury  in  the 

34 


PHYSICAL    PROPERTIES     OF    FLUIDS 

bowl.  The  elevation  of  the  mercury  in  the  columns  then 
indicates  the  atmospheric  pressure  as  the  vacant  space  above 
the  mercury  is  practically  a  vacuum.  If  the  whole  ap- 
paratus including  the  bowl  is  then  placed  in  a  glass  container 
connected  with  a  vacuum  pump  and  the  air  is  pumped  from 
the  container,  the  mercury  in  the  columns  will  fall  until  the 
air  in  the  container  is  exhausted  when  the  levels  of  the  mer- 
cury in  the  columns  will  nearly  reach  the  level  of  the  mercury 
in  the  bowl.  Due  to  leakage  etc.  it  will  never  be  possible 
to  obtain  a  condition  when  the  surfaces  will  be  on  the  same 
level.  The  condition  when  the  surfaces  would  be  level  is 
the  entire  absence  of  pressure  on  the  outside  of  the  tubes, 
the  perfect  vacuum  or  the  absolute  zero  of  pressure.  This 
point  is  called  the  zero  of  absolute  pressure.  See  Fig.  20. 

The  zero  point  of  absolute  pressure  is  a  perfect  vacuum. 
Like  the  zero  of  absolute  temperature,  it  does  not  exist  ex- 
cept theoretically.  To  express  pressures  in  absolute  units 
the  gauge  pressure  must  be  added  to  the  atmospheric  pressure. 
The  solution  of  all  problems  in  gas  measurement  is  greatly 
simplified  by  expressing  all  pressures  in  absolute  units.  To 
express  pressures  in  absolute  units  the  atmospheric  pressure 
must  be  added  to  the  gauge  pressure.  For  example  if  the 
gauge  pressure  is  10  Ib.  per  square  inch  and  the  atmospheric 
pressure  is  14.4  Ib.,  the  absolute  pressure  is  (10.0+14.4)  or 
24.4  Ib.  per  square  inch.  See  Fig.  20.  Likewise,  a  line 
pressure  of  20  inches  of  mercury  is  equal  to  an  absolute 
pressure  of  (20+29.34)  or  49.34  inches  of  mercury,  where  the 
atmospheric  pressure  is  29.34  inches  of  mercury. 

Atmospheric  Pressure  of  Gas  Fields — Some  years  ago 
Mr.  F.  H.  Oliphant,  at  that  time  of  the  United  States  Geo- 
logical Survey,  considered  as  a  basis  of  natural  gas  measure- 
ment a  pressure  of  14.65  pounds  per  square  inch  absolute, 
and  a  temperature  of  60  deg.  fahr.,  and  since  then  it  has 
become  customary  for  natural  gas  men  to  refer  their  gas 
measurements  to  this  basis.  A  pressure  of  14.65  pounds  per 

35 


PHYSICAL    PROPERTIES     OF    FLUIDS 

square  inch  is  4  ounces  above  the  assumed  atmospheric 
pressure  of  14.4  pounds  per  square  inch,  the  latter  being  the 
average  at  about  the  elevation  of  the  Great  Lakes,  which 
elevation  was  considered  as  fairly  representing  that  of  most 
gas  fields. 

Pressure  Gauges — The  pressure  acting  upon,  or  exerted 
by  fluids  is  expressed  usually  in  pounds  per  square  inch, 
inches  of  mercury,  inches  of  water  and  feet  head  of  fluid. 
It  is  indicated  by  spring  gauges,  siphon  gauges  or  U  tubes, 
and  sometimes  by  ordinary  vertical  columns  of  liquids. 

The  ordinary  gauge  spring  is  usually  made  of  light  hollow 
brass  tubing,  one  end  sealed,  coiled  in  form  of  a  horseshoe  or 
around  a  circular  rod,  the  open  end  being  fixed  to  suitable 
appliances  for  connections  to  pipes,  etc.,  in  which  is  contained 
the  fluid  whose  pressure  is  desired,  the  closed  end  being 
connected  to  an  indicating  pointer  or  pen  arm  either  directly 
or  by  means  of  levers.  When  the  pressure  on  the  inside  of 
the  tube  is  the  same  as  on  the  outside,  the  pointer  will  re- 
tain a  fixed  zero  position  but  as  pressure  on  the  inside  in- 
creases and  becomes  greater  than  the  outside  pressure  the 
tube  expands  and  tends  to  straighten  the  coil  causing  the 
arm  attached  to  the  sealed  end  to  rotate  by  equal  distances 
for  equal  increases  in  pressure.  Thus  a  spring  which  is  set 
at  zero  with  the  atmospheric  pressure  at  sea  level  acting  on 
the  inside  and  outside  will  retain  the  same  zero  position  on 
top  of  Pike's  Peak  when  open  to  the  atmosphere.  If  the 
gauge  is  placed  in  a  tight  container  under  pressure  with  the 
same  pressure  on  the  inside  and  outside  of  the  spring,  the 
pen  will  still  retain  its  zero  position.  Therefore,  a  spring 
gauge  is  a  differential  pressure  gauge,  that  is,  it  indicates  a 
difference  in  pressure.  This  difference  is  usually  above  and 
sometimes  below  atmospheric  pressure.  The  pressure  above 
atmospheric  pressure  is  generally  expressed  in  pounds  per 
square  inch  and  below  atmospheric  pressure  in  inches  of 
mercury  vacuum.  Gauges  are  marked  to  indicate  pressures 

36 


PHYSICAL    PROPERTIES     OF    FLUIDS 


Fig.  17— PRESSURE  SPRING.       STUFFING  BOX  OF   DIFFERENTIAL 
GAUGE  SHAFT  EXTENDING   THROUGH  CENTER    OF  SPRING 


Fig.  IS— PRESSURE  GAUGE  USED  FOR   TESTING 

37 


PHYSICAL    PROPERTIES     OF    FLUIDS 

in  various  units,  such  as  pounds  per  square  inch,  ounces  per 
square  inch,  inches  of  water,  feet  of  water,  etc. 

When  a  tap  is  made  in  a  line  containing  liquid  under  pres- 
sure and  a  vertical  tube  is  attached  to  the  line  the  liquid  will 
rise  in  the  tube  a  certain  height  depending  upon  the  pressure 
and  the  weight  of  the  fluid  per  unit  volume.  The  height 
will  increase  with  the  pressure.  Thus,  if  the  pressure  in  a 
water  line  is  ten  pounds ;  that  is,  ten  pounds  per  square  inch 
greater  than  the  atmosphere,  the  water  will  rise  277.1  inches 
(23.09  feet)  in  the  tube. 

For  small  differences  of  pressure  a  glass  U  gauge  is  used. 
Various  liquids  are  used  depending  upon  the  range  of  the 
gauge  and  character  of  fluid  whose  pressure  is  to 
be  determined.  The  pressure  difference  is  the 
difference  of  the  surfaces  of  the  liquids  in  the  col- 
umns of  the  U  tube.  If  mercury  is  used  in  the 
gauge  and  the  tube  C  is  connected  to  the  container 
of  fluid  with  D  open  to  the  atmosphere  the  pres- 
sure in  the  container  is  m  inches  of  mercury 
greater  than  the  atmosphere.  If  this  tube  is 
connected  across  an  orifice  in  which  a  liquid  is 
flowing,  for  example,  water,  and  each  column  and 
connecting  lines  D  and  C  are  filled  with  water 
above  the  mercury,  the  difference  in  height  of  the  surfaces 
of  the  mercury  does  not  represent  the  true  difference  in 
pressure  due  to  the  fact  that  difference  in  levels  m  is  partially 
offset  by  a  column  of  water,  m  inches  high,  in  the  opposite 
leg  A.  Therefore,  the  total  difference  in  pressure  is  equal 
to  m  inches  of  mercury  minus  m  inches  of  water  and  since 
each  inch  of  water  is  equal  to  .0735  inches  of  mercury,  the 
pressure  differential  is  m  — .0735  m  or  0.9265  m  inches  of 
mercury.  In  the  case  of  gases  the  fact  is  that  the  difference 
in  liquid  levels  in  the  U  tube  is  also  offset  by  a  column  of  m 
inches  of  air,  but  air  is  so  light  when  compared  with  liquids 
that  the  effect  is  entirely  disregarded. 


PHYSICAL    PROPERTIES     OF    FLUIDS 

Static  Pressure — In  orifice  meter  data  the  line  pressure 
above  the  atmosphere  is  usually  known  as  the  static  pressure 
or  standing  pressure,  to  distinguish  this  pressure  from  the 
differential  pressure  which  is  a  pressure  difference  due  to 
flow. 


50 


Ftg. 


Vacuum — Ordinary  use  of  this  term  means  merely  a 
partial  diminution  of  pressure  below  the  normal  atmospheric 
pressure  or  zero  gauge  pressure.  This  is  the  engineering 
conception  of  the  term  as  used  in  this  book.  The  maximum 
degree  attainable  with  ordinary  engineering  appliances  is 
about  14  pounds  below  atmospheric.  One  of  the  best  ex- 
amples of  vacuum  is  an  incandescent  light  bulb.  In  break- 
ing off  the  tip  after  placing  under  water,  the  bulb  is  nearly 

39 


PHYSICAL    PROPERTIES     OF    FLUIDS 


filled  with  water  because  the  water  is  under  the  pressure  of 
the  atmosphere,  and  the  interior  of  bulb,  prior  to  breaking,  was 
under  a  minus  pressure  or  less  than  atmospheric.  Vacuum 
is  usually  expressed  in  inches  of  mercury.  Reference  to 
Fig.  20  shows  that  vacuum  is  indicated  on  a  gauge  in  the 
reverse  direction  from  the  pressure.  One  inch  mercury 
vacuum  is  equal  to  —0.4908  Ib.  per  sq.  in.  Therefore,  the 
absolute  pressure  corresponding  to  mercury  vacuum  equals 
14.4 — .4908  X  (inches  of  mercury  vacuum)  when  the  atmos- 
pheric pressure  is  14.4  Ib.  per  sq.  in. 

Table  3 

Based  on  Atmospheric  Pressure  of  14.4  Ib. 


Gauge  Pressure 

Absolute  Pres- 

Vacuum Inches 

Absolute  Pres- 

Ib. per  sq.  in. 

sure  Ib.  per  sq. 

of  mercury 

sure  Ib.  per  sq. 

in. 

in. 

50 

64.4 

1 

13.91 

10 

24.4 

5 

11.95 

1 

15.4 

10 

9.49 

0.25 

14.65 

20 

4.58 

Referring  to  Fig.  21  in  which  there  are  two  U  gauges, 
if  the  closed  column  B  of  gauge  A  is  filled  with  mercury 
and  the  gauge  is  inverted,  then  gauge  A  will  indicate  the 
pressure  of  the  atmosphere  as  explained  on  Page  32. 
Assume  gauge  C  is  an  ordinary  siphon  gauge  in  which 
mercury  is  added  until  the  surfaces  of  the  mercury  rest 
at  point  E,  column  D  being  open  to  the  atmosphere,  and 
columns  F  and  G  of  the  two  gauges  being  connected  to  the 
same  vacuum  pump.  When  the  line  leading  to  the  vacuum 
pump  is  open  to  the  atmosphere  the  difference  in  height  of 
mercury  at  gauge  A  will  indicate  the  atmospheric  pressure. 
The  elevation  of  the  mercury  in  the  columns  of  gauge  C  will  be 
the  same,  indicating  that  the  pressures  on  columns  G  and  D 
are  equal.  As  the  vacuum  is  being  placed  on  the  columns  F 
and  G  thereby  removing  the  air  from  each  of  these  columns 

40 


p  H  Y  S  ICAL     PROPERTIES     OF    FLUIDS 

the  mercury  will  fall  in  columns  B  and  D  and  rise  in  columns 
F  and  G,  for  the  reason  that  the  pressures  acting  on 
columns  F  and  G  become  less  than  the  atmospheric  pressure. 
The  difference  in  height  m  of  the  surfaces  of  the  mercury  in 
the  columns  of  gauge  A,  will  then  indicate  the  absolute  pres- 
sure in  inches  of  mercury  acting  on  the  vacuum  line.  The 


s 

A 

F   & 

_i 
D 

Pressure 

— 

i 

<J 

TV 

— 

-£ 

1. 

1 

7J 

0 

_i 

E 

M 

J 

^ 

Fig.  21 

difference  in  height  of  the  surfaces  of  the  mercury  in  the 
columns  of  gauge  C  will  indicate  the  inches  of  mercury 
vacuum  n  exerted  by  the  vacuum  pump.  As  the  vacuum 
is  increased  and  if  it  were  possible  to  entirely  remove  the  air 
from  columns  F  and  G,  thereby  eliminating  all  pressure,  the 
elevation  of  the  surfaces  of  the  mercury  in  columns  of  gauge 
A  will  be  on  the  same  level  as  the  pressure  acting  on  each 
column  is  zero.  The  difference  in  height  of  the  surfaces  of 
mercury  in  gauge  C  would  indicate  the  atmospheric  pressure 
for  the  reason  that  there  is  no  pressure  whatever  in  column 
G  whereas  the  atmosphere  acts  on  surface  of  the  mercury  in 
column  D. 

41 


PHYSICAL    PROPERTIES     OF    FLUIDS 

This  arrangement  will  also  illustrate  the  fact  that  the 
inches  of  mercury  vacuum  when  expressed  as  absolute 
pressure,  is  dependent  upon  the  atmospheric  pressure.  If 
the  atmospheric  pressure  decreases,  the  difference  in  height 
at  gauge  A  will  decrease  when  the  line  leading  to  the  vacuum 
pump  is  open  to  the  atmosphere,  and  the  greatest  difference  in 
height  of  surfaces  of  the  mercury  in  gauge  C  when  connected 
to  the  pump  can  never  exceed  the  difference  in  elevations  of 
the  mercury  at  gauge  A  when  column  F  is  open  to  the  at- 
mosphere, providing  the  atmospheric  pressure  remains  the 
same.  So  consequently  it  is  impossible  to  obtain  a  greater 
number  of  inches  of  mercury  vacuum  than  the  atmospheric 
pressure  expressed  in  inches  of  mercury. 

As  an  example,  we  will  assume  that  when  the  apparatus  is 
open  to  the  atmosphere  that  gauge  A  indicates  an  atmospheric 
pressure  of  30  inches  of  mercury.  Gauge  C  will  then  indicate 
0  inches  of  mercury.  If  a  vacuum  of  20  inches  of  mercury 
is  placed  on  the  line  by  the  vacuum  pump  the  mercury  in 
column  D  will  fall  and  in  column  G  will  rise  until  the  dif- 
ference n  in  height  of  the  surfaces  is  20  inches.  At  the  same 
time,  mercury  in  column  B  will  fall  and  F  will  rise  until  the 
difference  in  height  is  10  inches.  So  therefore,  at  any  con- 
dition of  vacuum  the  sum  of  the  inches  of  mercury  dif- 
ferentials of  gauge  A  and  gauge  C  will  be  equal  to  the  at- 
mospheric pressure.  (10  inches +20  inches  =  30  inches). 

If  the  atmospheric  pressure  is  only  25  inches  of  mercury 
and  20  inches  of  mercury  vacuum  is  being  placed  on  the 
line  by  the  vacuum  pump  the  difference  in  height  at  gauge  C 
will  be  20  inches  and  at  gauge  A,  5  inches,  and  in  this  case 
the  sum  of  these  pressures  indicate  the  atmospheric  pressure 
(20+5  =  25.)  Therefore,  the  absolute  pressure  which  is 
represented  by  gauge  A  is  equal  to  the  atmospheric  pressure 
minus  the  vacuum  expressed  in  same  units.  Assume  the 
atmospheric  pressure  is  14.4  Ib.  per  square  inch,  20  inches 
of  mercury  vacuum  represents  9.8  Ib.  per  square  inch  vac- 

42 


PHYSICAL    PROPERTIES     OF    FLUIDS 


Table  4 
VACUUM— ABSOLUTE  PRESSURE 


Absolute  Pressure 

Inches 

Based  on  Atmospheric 

Based  on  Atmospheric 

Mercury 

Pressure  14.4  Ib. 

Pressure  14.7  Ib. 

Vacuum 

Inches  of 

Pounds  per 

Inches  of 

Pounds  per 

Mercury 

Sq.  In. 

Mercury 

Sq.  In. 

0 

29.34 

14.400 

29.95 

14.700 

1 

28.34 

13.909 

28.95 

14.209 

2 

27.34 

13.418 

27.95 

13.718 

3 

26.34 

12.928 

26.95 

13.228 

4 

25.34 

12.437 

25.95 

12.737 

5 

24.34 

11.946 

24.95 

12.246 

6 

23.34 

11.455 

23.95 

11.755 

7 

22.34 

10.964 

22.95 

11.264 

8 

21.34 

10.474 

21.95 

10.774 

9 

20.34 

9.983 

20.95 

10.283 

10 

19.34 

9.492 

19.95 

9.792 

11 

18.34 

9.001, 

18.95 

9.301 

12 

17.34 

8.510 

17.95 

8.810 

13 

16.34 

8.020 

16.95 

8.320 

14 

15.34 

7.529 

15.95 

7.829 

15 

14.34 

7.038 

14.95 

7.338 

16 

13.34 

6.547 

13.95 

6.847 

17 

12.34 

6.056 

12.95 

6.356 

18 

11.34 

5.566 

11.95 

5.866 

19 

10.34 

5.075 

10.95 

5.375 

20 

9.34 

4.584 

9.95 

4.884 

21 

8.34 

4.093 

8.95 

4.393 

22 

7.34 

3.602 

7.95 

3.902 

23 

6.34 

3.112 

6.95 

3.412 

24 

5.34 

2.621 

5.95 

2.921 

25 

4.34 

2.130 

4.95 

2.430 

26 

3.34 

1.639 

3.95 

1.939 

27 

2.34 

1.148 

2.95 

1.448 

28 

1.34 

0.6576 

1.95 

0.9576 

29 

0.34 

0.1668 

0.95 

0.4668 

43 


PHYSICAL    PROPERTIES     OF    FLUIDS 

uum,  therefore,  the  absolute  pressure  is  equal  to  4.6  Ib.  per 
square  inch  (14.4 — 9.8  =  4.6).  If  these  pressures  are  ex- 
pressed in  inches  of  mercury,  14.4  Ib.is  29.3  inches  of  mercury, 
then  20  inches  of  vacuum  represents  9.3  inches  mercury 
absolute  pressure  (29.3 — 20  =  9.3).  9.3  inches  mercury  abso- 
lute equals  4.6  Ib.  per  square  inch  absolute  (9. 3  X. 4908  =  4. 6). 
A  vacuum  will  cause  a  spring  to  coil  or  rotate  in  the  oppo- 
site direction  from  the  motion  occasioned  by  the  pressure. 
Mercury  vacuum  is  expressed  in  inches  of  mercury  below  the 
atmospheric  pressure  whereas  absolute  pressure  is  some- 
times expressed  in  inches  of  mercury  above  the  absolute  vac- 
uum so  that  the  absolute  pressure  of  a  fluid  under  a  vacuum 
is  equal  to  the  atmospheric  pressure  minus  the  vacuum. 
For  example,  if  the  atmospheric  pressure  is  29.4  and  fluid 
is  under  27  inches  vacuum  the  absolute  pressure  of  the  fluid  is 
2.4  inches  of  mercury  or  1.2  Ib.  per  square  inch. 

Pressure  Base — Under  the  caption  of  all  orifice  tables  in 
this  book  a  Pressure  Base  pb  is  specified.  The  calculations 
for  most  of  the  tables  were  made  by  adding  this  Base  to 
14.4  Ib.  the  average  atmospheric  pressure,  thus  a  4  oz.  base 
is  equivalent  to  14.4  Ib.  plus  0.25  Ib.  or  14.65  Ib.  per  square 
inch  absolute  pressure.  In  adding  the  pressure  base  to  the 
atmospheric  pressure  both  quantities  must  be  expressed  in 
pounds  per  square  inch. 

In  the  gas  business  a  Pressure  Base  is  specified  and  this 
pressure  is  the  basis  of  measurement  to  which  all  gas  vol- 
umes shall  be  calculated.  Thus,  a  cubic  foot  of  gas  at  29.8 
Ib.  absolute,  equals  2  cubic  feet  at  14.9  Ib.  or  at  8  oz.  above 
an  atmospheric  pressure  of  14.4  Ib.  per  square  inch. 

VELOCITY 

All  matter  is  in  motion.  There  is  no  such  thing  as  ab- 
solute rest  in  the  universe.  There  is  no  use  for  the  word 
rest,  except  to  indicate,  with  reference  to  each  other,  the 
conditions  of  objects  that  are  moving  in  the  same  direction 

44 


p  H  YSICAL    PROPERTIES     OF    FLUIDS 

and  with  the  same  velocity.  For  example,  the  cars  and 
engine  of  a  train  running  at  a  speed  of  30  miles  an  hour, 
are  at  rest  with  reference  to  each  other.  The  phrase  "at 
rest"  can  only  be  used  in  an  extremely  limited  sense,  and  in 
common  language  refers  only  to  the  condition  of  an  object 
with  reference  to  that  on  which  it  stands,  as  a  car,  deck  of  a 
ship,  or  surface  of  the  earth.  It  is  only  by  putting  entirely 
out  of  mind  the  motions  of  the  earth  that  we  can  speak  of 
any  terrestrial  object  as  being  at  rest. 

Not  only  is  there  motion  of  mass  as  a  whole,  or  visible 
mechanical  motion,  but  there  is  a  motion  of  the  molecules 
within  the  mass,  an  invisible  molecular  motion.  We  cannot 
see  the  movements  of  the  molecules  of  steam,  but  we  know 
that  they  exist  by  their  great  power,  manifested  in  moving 
machinery. 

Uniform  and  varied  motion — All  motion  takes  time; 
hence  the  term  velocity,  which  refers  to  the  space  traversed  in 
a  unit  of  time.  Motion  may  be  uniform  or  varied;  uniform, 
when  an  object  traverses  successively  equal  spaces  in  all 
equal  intervals  of  time;  varied,  when  unequal  spaces  are 
traversed  in  any  equal  intervals  of  time.  Varied  motion 
may  be  accelerated  or  retarded;  accelerated,  when  the 
spaces  traversed  increase  at  each  successive  interval  of 
time;  retarded,  when  they  diminish.  The  motion  of  a 
train  of  cars,  in  starting  from  a  station  is  at  first  accelerated, 
afterwards  tolerably  uniform,  and  when  the  brakes  are  ap- 
plied, it  becomes  retarded.  Strictly  speaking,  all  motions 
are  varied;  there  is  no  illustration  of  absolutely  uniform 
motion  in  Nature  nor  in  art,  though  we  may  conceive  of  its 
possibility  and  have  very  closely  approximated  to  it. 

Accelerated  motion  or  velocity — Even  if  several  men  push 
against  a  heavy  car  we  may  be  unable  to  recognize  any  mo- 
tion for  two  or  three  seconds;  but,  if  they  continue  to  exert 
force  upon  the  car,  it  will  move  with  greater  and  greater 
velocity  until  the  resisting  force  (which  increases  with  the 

45 


PHYSICAL    PROPERTIES     OF    FLUIDS 


velocity)  becomes  equal  to  that  applied  by  the  men.     This 
continually  increasing  velocity  is  termed  accelerated  velocity. 

Velocity  Head — All  particles  of  matter  are  attracted  to 
the  earth  by  gravity.  When  a  body  of  any  weight  or  density 
falls  to  the  earth  it  will  fall  approximately  16  feet  in  one 
second,  64  feet  in  two  seconds,  144  feet  in  three  seconds,  256 
feet  in  four  seconds,  and  400  feet  in  five  seconds,  etc.,  when 
not  acted  upon  by  friction  of  air.  These  facts  are  the  results 
of  numerous  experiments. 

It  is  noted  that  the  average  speed  per  second  increases  as 
the  time  of  falling  increases,  being  16  feet  per  second  for  one 
second,  32  feet  per  second  for  the  first  two  seconds.  Since 
the  velocity  at  the  start  was  zero  the  velocity  at  the  end  of 
the  first  second  must  be  32  feet  per  second  and  at  the  end  of 
two  seconds  64  feet  per  second  in  order  that  the  average  speed 
would  equal  16  feet  and  32  feet  per  second  respectively  for 
the  elapsed  periods. 

Acceleration  is  the  increase  per  second  in  velocity  per 
second.  The  velocity  increases  from  rest  0  feet  to  32  feet  per 
second  in  the  first  second  and  from  32  feet  to  64  feet  per  second 
during  the  second  second.  Therefore,  the  acceleration  due 
to  gravity  is  32  feet  per  second,  and  is  equal  to  the  velocity 
at  the  end  of  any  time  period,  divided  by  the  time.  See 
Table  5. 

Table  5 


Time 
Seconds 

H 
Feet 

Average  Velo- 
city in  ft.  per 
sec. 

Velocity  V  at 
end  of  time 
period  in  ft. 
per  sec. 

Acceleration* 
g    in    feet 
per  sec. 

0 

0 

0 

1 

16 

16 

32 

32 

2 

64 

32 

64 

32 

3 

144 

48 

96 

32 

4 

256 

64 

128 

32 

5 

400 

80 

160 

32 

*  The  average  value  of  §  used  in  calculations  in  this  book  is  32.16  except  where 
otherwise  designated. 

46 


PHYSICAL    PROPERTIES     OF    FLUIDS 


Let  V  represent  the  velocity  at  the  end  of  each  time  period 
t,  and  H  equal  distance  through  which  the  body  fell.      Then 

V 

the  average  velocity  =  — 
2i 

TJ 

The  average  velocity  also  equals  — 

Therefore  —  =  — 
/      2 

(a)       H=  V-Xt 

2i 

Which  fact  is  that  distance  equals  the  average  velocity 
multiplied  by  the  time.     But  the  velocity  at  the  end  of  each 
period  divided  by  the  acceleration  g  is  equal  to  the  time. 
V 

s 

Substituting  this  value  of  t  in  the  above  formula  (a) 


A  body  projected  upward  with  a  certain  velocity  will  rise 
to  a  height  equal  to  the  distance  through  which  it  would  have 

V2 
to  fall  to  acquire  this  velocity.     Therefore  —  is  known  as  the 

2£ 
velocity  head,  and  is  equal  to  H. 

Inasmuch  as  any  object  acquires  a  velocity  V  equal  to 
•\l2gH  in  falling  a  distance  H,  if  a  certain  amount  of  water 
fell  from  point  A  to  point  B  a  height  of  m  feet  as  represented 
in  Fig.  22  its  velocity  V  at  B  would  be  equal  to  ^J2gm  where 
m  =  H;  also  if  a  stream  of  water  is  projected  vertically  by 
velocity  at  point  B  the  height  to  which  it  would  rise  would 

F* 
be  equal  to  —  or  m  where  m  is  expressed  in  feet.     This 

47 


PHYSICAL    PROPERTIES     OF    FLUIDS 

statement  will  apply  to  any  fluid  providing  the  resistance 
due  to  the  air,  etc.,  is  eliminated.  Likewise,  if  the  vessel  shown 
in  this  figure  contained  a  liquid,  the  theoretical  velocity  of 
the  liquid  through  the  orifices  at  B  and  C  would  also  equal 
\2grn  theoretically  and  the  liquid  at  orifice  C  would  rise 
to  the  level  of  the  surface  of  the  liquid  at  A.  Although  the 
liquid  at  the  surface  A  does  not  pass  through  the  orifice,  a 
portion  of  the  lower  layer  of  liquid  passes  through  the  orifice 
and  consequently  the  height  of  liquid  is  lowered ;  the  portions 
passing  through  the  orifice  being  replaced  by  other  portions 
from  a  higher  level  and  this  same  operation  continuing  until 
we  reach  the  surface  of  the  liquid  so  that  the  effect  in  reality, 
is  the  same  as  if  the  liquid  from  the  surface  fell  through  the 
distance  m. 


Fig.  22 


The  total  pressure  on  the  liquid  on  the  inside  of  the 
vessel  at  points  B  and  C,  which  are  on  the  same  level,  equals 
the  pressure  of  atmosphere  acting  on  surface  of  liquid  at  A 
plus  the  pressure  due  to  the  height  of  liquid  m  above  the 
orifice.  The  pressure  acting  on  the  outside  of  the  vessel  or 
opposing  the  flow  of  the  liquid  through  the  orifice  is  the  at- 
mospheric pressure,  so  that  the  velocity  of  efflux  through  the 
orifice  is  equal  to  the  difference  in  the  pressure  on  the  inside 

48 


PHYSICAL    PROPERTIES     OF    FLUIDS 

of  the  vessel  at  points  B  and  C,  and  the  pressure  on  the  outside 
of  the  vessel  at  the  same  points,  which  difference  is  equal  to 
the  head  of  liquid  m. 

If  the  orifice  B  opened  into  a  vessel  which  was  under  a 
perfect  vacuum,  where  the  total  pressure  was  zero  pounds  to 
the  square  inch,  the  difference  of  pressure  between  the  inside 
and  outside  of  the  vessel  would  be  equal  to  the  atmospheric 
pressure  plus  the  head  m,  the  outside  pressure  being  zero. 
Therefore,  since  the  atmospheric  pressure  is  equivalent  to  a 
head  of  34  feet  in  case  of  water  at  sea  level,  the  total  pres- 
sure or  head  on  the  orifice  C  producing  the  velocity  through 
the  orifice  would  be  34  plus  m  or  the  theoretical  velocity  of 
exit  would  be  eq ual  to  V  2g (34 + m)  for  water .  H  =  34:-\-m. 

Again  we  will  assume  that  the  orifice  B  opened  into  a 
vessel  in  which  the  same  liquid  was  contained  and  the 
height  of  the  liquid  in  this  vessel  was  two  feet  above  the 
elevation  of  the  orifice.  In  this  case  the  difference  in  pres- 
sure between  the  inside  of  the  vessel  at  the  orifice  and  the 
outside  of  the  vessel  at  the  orifice  would  be  m — 2  feet,  in 
which  case  the  velocity  through  the  orifice  would  be  equal  to 
the  V'2g(w— 2). 

As  another  example  we  will  assume  that  the  opening  D 
is  attached  to  an  air  line  from  a  compressor  and  that  a 
pressure  of  50  pounds  per  square  inch  is  exerted  upon  the  sur- 
face of  the  liquid  as  shown  by  the  gauge  E,  and  that  the  li- 
quid flows  into  the  atmosphere  through  the  orifices  B  and  C. 
In  this  case  the  total  pressure  on  the  surface  of  the  liquid 
would  be  equal  to  50  pounds  plus  the  atmosphere.  As  one 
pound  per  square  inch  equals  2.3  feet  head  in  case  of  water, 
50  pounds  would  be  equal  to  115  feet  head  which  is  the 
height  that  the  water  will  rise  in  the  open  tube  G  above  the 
surface  of  water  at  A.  The  total  pressure  at  B  would  be 
equal  to  w  +  115  feet  plus  34  feet  due  to  the  atmospheric 
pressure.  The  pressure  on  the  outside  of  the  vessel  is  equal  to 

49 


PHYSICAL    PROPERTIES     OF    FLUIDS 

the  atmospheric  pressure  or  34  feet  so  that  the  difference  in 
pressure  between  the  inside  and  outside  or  the  differential 
pressure  causing  the  flow  through  the  orifice  is  equal  to  115 
plus  m  feet.  This  is  the  pressure  which  would  be  registered 
on  the  gauge  at  F,  or  the  pressure  is  equivalent  to  that  which 
would  exist  if  the  vessel  were  increased  in  height  and  the 
elevation  of  the  liquid  above  point  A  would  be  115  feet. 

From  the  above  discussion  it  is  seen  that  the  velocity 
through  an  orifice  for  any  liquid  is  equal  to  V  2gH,  in  which 
H  equals  the  differential  in  feet  head  of  liquid  existing  be- 
tween the  two  sides  of  the  orifice.  The  velocity  in  the  case 
above  mentioned  is  the  theoretical  velocity.  Due  to  friction, 
etc.,  the  velocity  is  less  than  the  theoretical  velocity.  Due 
to  contraction  of  the  jet  the  total  volume  flowing  is  less 
than  the  theoretical  volume  which  would  be  obtained  by 
multiplying  the  area  of  the  orifice  by  the  theoretical  velocity. 
Most  books  on  hydraulics  and  physics  divide  the  difference 
between  the  actual  and  theoretical  by  applying  two  sets  of 
multipliers  or  coefficients,  one  for  contraction  of  the  jet  and 
the  other  for  the  decrease  of  velocity  due  to  friction,  etc. 
However,  in  all  discussions  dealing  with  the  flow  of  fluids 
by  orifice  meter  only  one  coefficient  Cv  is  used  and  this  is 
termed  the  "coefficient  of  velocity."  Cv  is  the  ratio  of  the 
average  velocity  of  the  fluid  passing  the  upstream  plane  of 
the  orifice  to  the  theoretical  velocity  as  determined  by  the 
formula  V=  ^2gH.  It  is  sometimes  called  the  efficiency 
of  the  orifice.  However,  since  this  definition  of  the 
"coefficient  of  velocity,"  has  been  accepted  by  nearly  all  gas 
engineers,  it  is  used  in  this  sense  throughout  this  book. 


50 


PHYSICAL    PROPERTIES     OF    FLUIDS 


DEG 
572 


TEMPERATURE 

The  ordinary  Fahrenheit  thermometer  is  made  and 
calibrated  by  partly  filling  a  glass  tube  terminating  in  a  bulb 
with  some  liquid,  usually  mercury,  and  sealing.  It  is  cooled 
to  a  temperature  of  melting  ice  or 
freezing  water  at  sea  level.  The 
point  at  which  the  top  of  the  mercury 
column  rests  is  marked  32  degrees  on 
the  tube.  It  is  then  heated  or  placed 
in  boiling  water  at  sea  level  and  the 
point  at  which  the  mercury  rests  is 
indicated  as  212  degrees.  The  bore 
of  the  tube  being  uniform,  the  space 
between  the  freezing  point  and  boiling 
point  is  divided  into  180  parts,  each 
division  representing  one  degree. 

Absolute  Temperature — It  was 
noted  by  early  experimenters  that  a 
definite  quantity  of  gas  occupying  a 
certain  volume;  for  example,  6  cu.  ft. 
at  140  deg.  fahr.  at  any  definite  pres- 
sure, upon  being  cooled  to  90  deg. 
fahr.  only  occupied  5.5  cu.  ft.  and  at 
the  same  pressure,  further  cooling  to 
40  deg.  fahr.  reduced  the  volume  to 
5  cu.  ft.,  and  at  60  deg.  below  zero 
the  volume  was  4  cu.  ft.  Therefore 
for  each  100  degrees  drop  in  tempera- 
ture below  the  140  deg.  fahr.  the  vol- 
ume decreased  one  cubic  foot  or  one- 
sixth  of  the  original  amount  so  that 
theoretically  at  600  degrees  below  140 
deg.  fahr.  or  at  460  deg.  below  zero  the 
volume  should  be  zero.  It  is  not  possible  to  produce  such  a 
condition,  but  numerous  experiments  have  indicated  similar 

51 


!-== 

-=^ 

_H- 

H 

H 

E1 

DEG. 
212 


100 


60 


32  Freezing 


OZero 


-SO 


-100 


-ISO 


-300 


-400 


Zero 


Fig. 


PHYSICAL    PROPERTIES     OF    FLUIDS 


results,  and  460  degrees  below  the  zero  of  the  ordinary  thermo- 
meter scale  has  been  designated  as  the  zero  of  the  f  ahrenheit 
absolute  scale.  The  use  of  the  absolute  scale  enables  us  to 
simplify  all  calculations  with  respect  to  gas  volumes  to  a 
minimum.  The  absolute  temperature  scale  is  expressed  in 
degrees  above  the  absolute  zero  being  equal  to  460  plus  the 
ordinary  commercial  scale. 

The  previous  data  is  compiled  in  the  following  Table: 
Table  6 


Temperature  Ordinary 
Scale 

Degrees  Fahrenheit 
Absolute  Scale 

Volume  Cubic 
Feet 

140 
90 
40 
60  below  zero 
460  below  zero 

600 
550 
500 
400 
0 

6.0 
5.5 
5.0 
4.0 
0.0 

This  table  indicates  that  the  same  weight  of  gas  at  the  same 
pressure  occupies  volumes  directly  proportional  to  the  absolute 
temperature. 

Various  experimenters  have  determined  the  absolute 
zero  at  various  values  from  459.2  to  459.6  deg.  fahr.  below 
zero,  but  as  460  has  been  used  in  nearly  all  gas  calcu- 
lations, this  value  is  retained  in  this  book.  Therefore,  the 
absolute  temperature  is  obtained  by  adding  460  degrees  to 
the  ordinary  Fahrenheit  scale.  80  deg.  fahr.  =  80+460,  or 
540  deg.  fahr.  absolute,  190  deg.  below  zero  is  equal  to 
—190+460,  or  270  deg.  fahr.  absolute. 

Temperature  Base — In  the  gas  business  a  temperature 
base  is  usually  specified.  The  usual  value  is  60  deg.  fahr. 
signifying  that  the  standard  basis  of  measurement  shall  be 
at  that  temperature  or  that  all  gas  volumes  shall  be  changed 
by  calculation  and  expressed  in  cubic  feet  at  60  deg.  fahr. 

52 


PHYSICAL    PROPERTIES     OF    FLUIDS 

To  use  this  value  in  calculations  it  must  be  expressed  in  the 
absolute  scale.  All  tables  state  the  base  tb  on  which  the 
calculations  are  made  according  to  the  ordinary  thermometer. 
To  obtain  the  absolute  value  Tb,  add  460  degrees.  60  deg. 
fahr.  is  520  deg.  fahr.  absolute. 

PERFECT  GASES 

In  the  illustrations  which  follow,  showing  by  diagram 
the  action  of  the  various  laws  of  perfect  gases,  we  assume  a 
cylinder  which  is  a  non-conductor,  fitted  with  a  frictionless 
piston  fitting  so  closely  that  it  does  not  permit  the  escape 
or  entrance  of  any  gases.  In  each  instance  the  contained 
gas  is  one-half  of  a  pound  of  air.  It  will  be  noticed  that  in 
each  example  the  gauge  pressure  acts  downward  on  the  pis- 
ton or  tending  to  compress  the  gas  and  that  in  the  case  of  a 
vacuum  the  force  is  assumed  to  act  upward,  that  is  to  say 
there  is  a  pull  on  the  piston  instead  of  a  pressure  being  ap- 
plied. The  pressure  of  the  atmosphere  is  acting  with  the 
gauge  pressure  to  produce  the  gross  or  absolute  pressure. 
In  the  cases  of  vacuum  the  force  applied  is  working  against 
the  atmosphere  or  the  pulling  force  plus  the  pressure  of  the 
contained  gas  just  equals  the  pressure  exerted  by  the  at- 
mosphere. 

Charles'  Law — The  volume  of  a  given  mass  or  volume 
in  cubic  feet  per  pound,  of  any  gas  under  any  constant  pres- 
sure increases  proportionately  as  the  absolute  temperature 
increases,  and  decreases  proportionately  as  the  absolute 
temperature  decreases.  See  Page  52. 

Referring  to  Figs.  24,  25  and  26,  it  will  be  seen  that  if  the 
gas  is  cooled  from  1080  deg.  fahr.  absolute  to  540  deg.  fahr. 
absolute,  the  volume,  without  in  any  way  altering  the  pres- 
sure, will  be  decreased  one-half.  Therefore,  the  volume  di- 
vided by  the  absolute  temperature  is  a  constant  for  any  gas, 
at  the  same  pressure. 

53 


PHYSICAL     PROPERTIES     OF    FLUIDS 


where  v  =  volume  per  pound  in  cubic  feet. 

T  =  Temperature  in  deg.  fahr.  absolute. 
c  =  a  constant  depending  upon  the  pressure. 
Therefore,  at  one  degree  absolute  the  volume  would  be 
c  cubic  feet. 


Abso/ute  Temperature 


Fig.  24 


Mt/meperib  /Oca  ft 
Fig.  25 


Atso/uGe  Temperature 

270Oeq.ffafjr. 
W6percu.ft20it>. 


Fig.  26 


The  formula    —  =    c    is    applied   to   the    above     figures 
as  follows: 


Fig. 
24 
25 
26 


v    T 

20  -5-1080  =  .0185  ) 
10-5-  540  =  .0185 
5-5-  270  =  .0185 


Value  of  c  for  air  at  20  Ib.  per 
j  sq.  in.  absolute. 


Table  7 

Table  showing  decrease  of  volume  and  increase  of  weight  per 
cubic  foot  of  air,  at  same  pressure  as  temperature  decreases. 


Temperature  deg.  fahr. 

Volume  of  one 
Ib.  in  cu.  ft. 

Weight,  Ib.  per 
cu.  ft. 

Absolute 

Ordinary 

1080 
540 
270 

620 
80 
-190 

20 
10 
5 

0.05 
0.10 
0.20 

54 


PHYSICAL    PROPERTIES     OF    FLUIDS 

The  fact  that  the  volume  divided  by  the  absolute  tem- 
perature is  a  constant  for  any  certain  gas  at  a  certain  pres- 
sure leads  to  the  following  statement, 

v  n        V 

~Tn==T==C 

in  which  vn  and  Tn  are  the  conditions  at  any  volume  and 
temperature  at  the  same  pressure,  then 

..-* 

Let  us  assume  that  the  volume  of  a  certain  weight  of  gas  is 
400  cu.  ft.  at  40  deg.  fahr.  at  a  certain  pressure.  The 
volume  vn  at  60  deg.  fahr.  would  be 

Wn  =  !!?J!  =  400X  —  -416  cu.  ft. 
T  500 

Boyle's  or  Mariotte's  Law — The  volume  of  a  given  body 
of  gas  depends  upon  the  pressure  to  which  it  is  subjected. 

At  twice  the  absolute  pressure  there  is  half  the  volume, 
while  the  density  and  elastic  force  are  doubled.  At  half  the 
absolute  pressure  the  volume  is  doubled,  and  the  density  and 
elastic  force  are  reduced  to  one-half.  Hence  the  law:  the 
volume  of  a  body  of  gas  varies  inversely  as  the  pressure, 
density,  or  elastic  force.  This  is  sometimes  called  Mariotte's 
and  sometimes  Boyle's  law,  from  the  names  of  two  men  who 
discovered  it  at  about  the  same  time. 

This  law  is  true  for  all  gases  within  certain  limits,  but  under 
extreme  pressure  the  reduction  in  volume  is  greater  than 
indicated  by  it.  The  greatest  deviation  from  it  occurs  with 
those  gases  that  are  most  easily  liquefied.  , 

The  product  of  the  absolute  pressure  multiplied  by  the 
volume  of  a  given  weight  of  gas  is  a  constant. 

Pv  =  k 

where  P  —  absolute  pressure  in  pounds  per  cubic  foot. 
v  =  volume  per  pound,  in  cubic  feet. 
k  =  a  constant  depending  upon  the  temperature. 

55 


PHYSICAL    PROPERTIES     OF    FLUIDS 

Therefore,   at  one  pound  per  sq.  in.  absolute  v  =  k  cubic 
feet.     See  Table  8  and  Figs.  27,  28  and  29. 


Table  8 

Showing  increase  of  volume  per  pound  and  decrease  of  weight 
per  cubic  foot  of  air  as  pressure  decreases  at  same  temperature 
(80  deg.  fahr.)  540  deg.  absolute. 


Pressure 

Volume  in  cubic 

Weight  in  Ib. 

Absolute, 
Ib.  per  sq.  in. 

Gauge 

feet  of  one  Ib. 
of  air. 

per  cubic  foot. 

40 

25.6  Ib.  persq.  in. 

5 

.20 

20 

5.6  Ib.  persq.  in. 

10 

.10 

10 

9  in.  mer.  vac. 

20 

.05 

.. 

W6.percu.ft.  .20Lb. 
per  it.  Scvfli 


Fig.  27 


Mume  pertf  /Ocuff. 
Fig.  28 


SODegfarir 

per  caft  .OSit 

Vo/t/meperlt>  ZOcu.fe 

Fig.  29 


The   formula   Pv  =  k   is  applied  to  the  above  figures  as 
follows : 


Fig. 

27 
28 
29 


P  V 

40     X       5  =  200 
20     X     10 


10     X     20  =  200 


.. 

j      deg 


of  k  for  air  at  540 
.  ..  11, 

'  fahr'   absolute' 


56 


PHYSICAL    PROPERTIES     OF    FLUIDS 


The  fact  that  the  absolute  pressure  multiplied  by  the 
volume  of  a  given  weight  of  gas  is  a  constant,  can  be  ex- 
pressed as  follows  : 

Pnvn  =  pv  =  k   where   Pn  and   vn   are  the  new   pressures 

Pv 
and  volumes  respectively  then  vn  =  — 

** 

If  the  absolute  pressure  of  a  certain  definite  weight  of  gas  is 
30  Ib.  per  square  inch  absolute  and  its  volume  is  120  cu.  ft. 
at  60  deg.  fahr.  the  volume  at  20  Ib.  per  square  inch  absolute 
at  60  deg.  is 

Wn  =  ^  =  30X—  =180cu,  ft. 
P.  20 


Relation  between  Absolute  Temperature  and  Absolute 
Pressure — As  the  absolute  temperature  decreases  for  a  defi- 
nite volume  of  gas,  the  absolute  pressure  decreases  at  the 
same  rate  and  vice  versa.  That  is,  the  absolute  pressure 
divided  by  the  absolute  temperature  is  a  constant  or  the 
absolute  temperature  divided  by  the  absolute  pressure 
is  a  constant.  This  is  illustrated  by  the  table  and  diagram 
following. 

Table  9 

Table  showing  decrease  of  pressure  as  temperature   decreases, 
volume  remaining  constant. 


Absolute  temp, 
deg.  fahr. 

Temperature 
deg.  fahr. 

Absolute  Pres- 
sure Ib.  per  sq. 

Gauge  Pressure 

in. 

1080 

620 

40 

25.6  Ib.  per  sq.  in. 

540 

80 

20 

5.6  Ib.  per  sq.  in. 

270 

-190 

10 

9  inch  vacuum. 

57 


PHYSICAL    PROPERTIES     OF    FLUIDS 


'  we.  per cu  fC  JO  It. 
Wvmepertii  /Oct/.ft 

Fig.  80 


ive  percuft  JOLt>. 
Vo/vmeperiti  /Oct/ft 


Fig.  31 


we  per  cu  ft. /O  it>. 
Vo/umeperib  /Ocuft 

Fig.  32 


lOcu. 


.per 


The  above  relation  may  be  shown  as  follows: 
Fig.  P  T 

30  40     +     1080  =.037  ' 

31  .20     +       540  =  .037 

32  10     +       270=037 

Since  the  pressure  divided  by  the  temperature  for  a  cer- 
tain definite  volume  of  gas  is  a  constant,  the  relation  may 
be  expressed: 

P      P 

—  =  —  =  a  constant 

Tn       T 

In  which  Pn  and  Tn  are  the  new  pressures  and  tempera- 
tures respectively. 


If  a  certain  volume  of  gas  at  a  temperature  of  40  deg.  fahr. 
(500  deg.  absolute)  under  a  pressure  of  30  Ib.  per  square  inch 
absolute,  is  heated,  the  pressure  of  the  same  volume  of 
gas  at  a  temperature  of  140  deg.  fahr.  (GOO  deg.  absolute) 
would  be  as  follows  : 

P  T  fiOO 

PM  =  —  "  =  30X  —  =  36  Ib.  per  square  inch  absolute. 
T  500 


58 


PHYSICAL    PROPERTIES     OF    FLUIDS 

Law  of  Perfect  Gases  —  Let  us  assume  the  theoretical  vol- 
ume of  a  pound  of  a  certain  ideal  gas  at  one  deg.  fahr. 
absolute  under  a  pressure  of  one  pound  per  square  inch 
absolute  is  Z  cubic  feet;  then,  according  to  Charles'  Law, 
the  volume  increases  as  the  absolute  temperature  increases, 
the  volume  at  an  absolute  temperature,  T  degrees,  will 
be  TZ  cu.  ft.  at  one  Ib.  per  square  inch  absolute  pressure. 
But  according  to  Boyle's  Law  the  volume  decreases  pro- 
portionately as  the  absolute  pressure  increases,  so  that  if 
the  pressure  is  increased  to  a  pressure  P  at  an  absolute  tem- 

TZ 

perature  J1,  the  volume  per  pound  v  =  — 

TZ 

—  =v 
P 

By  transposing  —  =  Z 


where  Pn,  vn  and  Tn  represent  the  pressure,  volume  and  tem- 
perature of  the  same  gas  at  other  conditions  than  those 
represented  by  P,  v  and  T, 

PvT 

therefore,  vn  =  —  - 
PnT 

If  the  volume  of  a  certain  weight  of  gas  is  20  cu.  ft.  at  10  Ib. 
per  square  inch  absolute  at  a  temperature  of  40  deg.  fahr., 
(absolute  temperature  500  degrees),  the  volume  at  60  deg. 
fahr.  (520  deg.  absolute)  under  a  pressure  of  26  Ib.  per  sq. 
inch  absolute  would  be 


PnT        26X500 

Therefore,  for  a  unit  weight  of  gas  the  product  of  the  volume 

59 


PHYSICAL    PROPERTIES  OF    FLUIDS 

v  multiplied   by  the   absolute  pressure  P  divided  by  the 

absolute  temperature  T  is  a  constant  Z.  The  value  of  Z  for 
air  is  0.37  approximately. 


for  air  using  one  pound  the  expression  becomes  —  a  =  .37 

where  P  =  absolute  pressure  in  pounds  per  square  inch  . 
va  =  volume  in  cubic  feet  of  one  pound  of  air. 
T  =  absolute  temperature  in  deg.  f  ahr. 

The  specific  gravity  of  a  fluid  is  the  ratio  of  the  weight 
of  a  cubic  foot  under  the  same  pressure  and  temperature 
conditions  to  the  weight  of  a  cubic  foot  of  another  fluid 
used  as  a  standard  or  base.  For  gaseous  fluids  air  is  gen- 
erally used  as  a  base  and  consequently  its  specific  gravity  is 
considered  1.00.  For  liquids  water  is  used  as  a  base  and  its 
specific  gravity  is  considered  1.00  at  point  of  maximum 
density. 

Returning  to  the  above  formula  in  which  va  represents 
volume  of  cubic  feet  occupied  by  a  pound  of  air,  it  can  be 
readily  understood  that  if  the  specific  gravity  of  a  gas  is 
less  than  air,  the  volume  of  a  pound  is  greater  proportion- 
ately than  of  a  pound  of  air.  If  v  represents  the  volume  of 
a  pound  of  the  gas 

^a  r- 

D  =  ~  or  va  =  vG 
G 

Substituting  in  the  above  expression  vG  for  va, 

we  obtain  -  =  .37 
T 

The  product  of  the  absolute  pressure  in  pounds,  volume 
per  pound  and  specific  gravity  of  any  gas  divided  by  its 
absolute  temperature,  is  equal  to  .37. 

60 


PHYSICAL    PROPERTIES     OF    FLUIDS 

=  .37JT 

PG 

The  volume  of  a  pound  of  gas,  at  60  deg.  fahr.,  specific 
gravity,  .60  under  a  pressure  of  14.4  absolute  is 

.37J     .37X520      00  0  , 

v  = = =22.2  cubic  feet. 

PG      14.4X.60 

~D    f~* 

Applying  the  formula  -    -  in  examples  given  in  which 

air  was  the  gas  under  consideration,  (specific  gravity  1.00) 
the  following  results  are  obtained. 


Constant  Pressure.     Figs.  24,  25  and  26 
PvG     20X20X1     20X10X1     20X5X1 


T  ~        1080  540  270 


=  .37 


Constant  Temperature.     Figs.  27,  28  and  29 
Pi)G    40X5X1     20X10X1     10X20X1 


T  540  540  540 


=  .37 


Constant  Volume  per  pound  or  Constant  Weight  per 

cubic  foot.       Figs.  30,  31  and  32 
PvG     40X10X1     20X10X1     10X10X1 


1080  540  270 


•=.37 


It  is  noticed  that  if  the  value  of  any  term  in  this  char- 
acteristic equation  is  changed  the  value  of  one  or  more  of  the 
others  must  change.  A  clear  understanding  of  this  equation 
and  its  derivatives  will  eliminate  most  of  the  troubles  now 
experienced  in  the  application  of  the  various  factors  used  in 
measurement  of  gases.  The  only  term  in  this  equation  which 
cannot  be  readily  determined  in  the  field  is  v.  Its  value  can 
easily  be  calculated,  and  even  so,  its  value  is  not  generally 
required. 

61 


PHYSICAL    PROPERTIES     OF    FLUIDS 

PRESSURE  DUE  TO  HEAD  OF  GAS 

Due  to  the  universal  expansibility  of  gas,  in  order  to  keep 
the  gas  from  diffusing  it  is  necessary  to  confine  it  in  an  in- 
closed vessel.  Let  the  vessel  ABCD  be  filled  with  air  at 
atmospheric  pressure.  Due  to  the  light  weight  per  cubic  foot 
it  is  generally  assumed  that  the  weight  of  a  cubic  foot  at  the 
top  of  the  vessel  would  be  the  same  as  the  weight  of  a  cubic 
foot  at  the  bottom  of  the  vessel.  This  statement  is  not 
strictly  true  for  the  reason  that  the  air  itself  weighs  something, 
and  the  weight  of  the  upper  layers  tend  to  compress  each 
lower  layer.  Assuming  that  the  air  is  uniform  in  density, 
and  that  the  pressure  acting  on  the  air  by  the  walls  of  the 
container  is  equal  to  the  atmospheric  pressure,  the  pressure 
acting  on  the  surface  CD  would  be  equal  to  the  pressure  on 
the  surface  AB  which  is  the  pressure  acting  on  the  gas  at  AB 
plus  the  weight  of  the  air  contained  in  the  vessel,  so  that  on 
each  square  inch  of  surface  CD,  the  pressure  is  equal  to  the 
pressure  per  square  inch  acting  at  AB  plus  the  weight  of  a 
column  of  the  air  one  inch  square  AC  in  height. 


Fig.  S3 

Air  at  atmospheric  pressure  weighs  approximately  ^  of  a 
pound  at  60  deg.  fahr.  so  that  if  AC  is  1872  feet  the  pressure 
acting  on  each  square  foot  on  the  surface  CD  is  144  pounds 
greater  than  the  pressure  per  square  foot  on  AB  or  one  pound 
per  square  inch  greater  than  on  AB  so  that  1872  feet  head  of 
air  is  equal  to  one  pound  per  square  inch  or  144  pounds  per 
square  foot.  Therefore,  the  head  of  gas  may  also  be  ex- 

62 


PHYSICAL    PROPERTIES     OF    FLUIDS 

pressed  in  pounds  per  square  inch  or  the  pressure  in  pounds 
per  square  inch  may  be  expressed  in  feet  head  of  gas  (at  a 
certain  pressure  and  temperature  of  the  gas). 

Pressures  and  Gas  Heads 

From  the  preceding  articles  it  is  evident  that  the  pressure 
head  of  any  fluid  may  be  expressed  in  terms  of  head  of  any 
other  fluid  or  it  may  be  expressed  in  terms  of  weight  per 
square  inch.  The  units  of  weight  used  throughout  this  vol- 
ume are  (unless  otherwise  stated) 

1  cubic  foot  of  water  at  62  deg.  fahr.  weighs  62.355  Ib. 
per  sq.  inch. 

1  cubic  foot  of  air  at  60  deg.  fahr.  at  14.7  Ib.  pressure 
weighs  .076381  Ib.  per  cubic  foot. 

Therefore,  a  column  of  water  one  square  foot  in  area,  one 

62  355 

foot  high,  is  equal  to or  816.37  feet  of  air  at  60  deg. 

.076381 

fahr.  at  14.7  Ib.  per  square  inch,  one  square  foot  in  area.  In- 
asmuch as  air  or  any  gas  increases  in  volume  as  the  absolute 
pressure  decreases,  one  foot  of  water  will  equal  816.37X14.7 
or  12000  feet  of  air  at  60  deg.  fahr.  at  one  pound  absolute 
pressure.  Therefore,  one  inch  of  water  is  equal  to  1000  feet 
of  air  at  60  deg.  fahr.  at  one  pound  per  square  inch  absolute 
pressure.  From  the  laws  of  perfect  gases,  for  any  other  pres- 
sure one  inch  of  water  is  equal  to  -  —  in  which  P  is  the  ab- 
solute pressure  in  pounds  per  square  inch.  For  any  other 
temperature  than  60  deg.  fahr.,  since  the  volume  of  air  in- 
creases as  the  absolute  temperature  increases,  the  head  in 

1 000          T 

feet  of  air  would  equal X in  which  T  would  be  the 

P          520 

absolute  temperature  in  deg.  fahr.  and  520  the  absolute 
temperature  corresponding  to  60  deg.  fahr. 

63 


PHYSICAL    PROPERTIES     OF    FLUIDS 


One  inch  of  water  = feet  head  of  air,  and  since 

520P 

the  volume  per  pound   decreases  as  the  specific  gravity  G 

1000  T  , 

increases,  one  inch  of  water  =  —        -  feet  of  any  gas. 

520  PG 

When   //  =  differential    in    feet    head    of    gas   and    h  = 
differential  in  inches  of  water, 

1000  hT 
~  520  PG 
Example,  Gas. 

Differential,  3  inches  of  water. 

Specific  Gravity,  .80.     Atmospheric  Pressure,  14.4  Ib. 
Gauge  Pressure,  48.1  Ib.     Temp.,  60  deg.  fahr. 
Solution:     P  =  48.1  +  14.4  =  62.5  Ib.  per  sq.  in.  abs. 
T  =  60+460  =  520  deg.  fahr.  abs. 

1000  hT     1000X3X520 

3  inches  of  water  = -  =—  -  =60 ft.  head 

520  PG      520X62.5X.80 

of  gas  at  the  temperature  and  pressure  stated. 


VELOCITY  HEAD  OF  FLOWING  GASES 

Just  as  the  velocity  of  efflux  through  an  orifice  is  pro- 
portional to  the  differential  pressure  between  the  liquid 
pressures  on  the  two  sides  of  the  orifice,  expressed  in  feet 
head  of  flowing  liquid,  the  velocity  of  the  flow  of  gases  obeys 
the  same  laws  in  that 


in  which  case  H  is  the  differential  in  feet  head  of  flowing 
gas  at  the  pressure  and  temperature  existing  either  at  the  in- 
let side  or  the  outlet  side  of  the  orifice.  In  orifice  meter 
measurements  the  percentage  differences  between  these 
pressures  are  very  small.  With  some  types  of  connections  the 
upstream  pressure  is  used  and  with  the  other  types  the  down- 
stream pressure  is  used. 

64 


PHYSICAL    PROPERTIES     OF    FLUIDS 

As  an  example  of  the  theoretical  flow  of  gas  at  60  deg. 
fahr.  assume  a  container  of  air,  the  pressure  on  the  upstream 
side  of  the  orifice  as  50  Ib.  per  square  inch  absolute  and 
the  pressure  on  the  downstream  side  as  49.82  Ib.  per  square 
inch.  Then  the  difference  in  pressure  is  .18  Ib.  or  5  inches 


of  water  (.18X27.71  —  5).    One  inch  of  water  equals 


1000 


or 


20  feet  of  air  at  50  Ib.  absolute  pressure,  at  60  deg.  fahr. 

Therefore  #  =  20X5  inches  of  water  or   100  feet   head 
of  air, 


and  V=  V2gX100  or  7  =  80  feet  per  second  as  the 
theoretical  velocity  of  the  air,  each  cubic  foot  passing  the 
orifice  at  50  Ib.  absolute  pressure,  at  60  deg.  fahr. 


Fig.  34 


65 


PHYSICAL    PROPERTIES     OF    FLUIDS 


Ilk* Out  CM* 

uated  to  50  inche*  of  Water 
Differential  Pre»ure.  Grad- 
uatioru  L16  Inch  which  per- 


Tap  for  By-Paw  and 
Connection  with  down 
ttream  .ide  of  Orifice.  x 


Double  prenure 
hart,  with  Differential  pre.- 
Graduationi  printed  in 
italic  printed  in 
black  ink. 


Fluted    iro, 
Nearly  frictionlcw. 


NTwo  inch  pipe 
thread  for  pipe  standard 
over  p,pe  line. 


Fig.  35— SECTIONAL  VIEW  OF  A  50  INCH  DIFFERENTIAL  GAUGE 
CONCENTRIC  CHAMBERS 


66 


PART    THREE 

ORIFICE  METER  MEASUREMENT 

GENERAL— ORIFICES  —  DETERMINATION  O  F 
ORIFICE  COEFFICIENTS  — MEASURING  FLOW  OF 
FLUIDS  —  DIFFERENTIAL  GAUGES  —  ACCURACY 
OF  ORIFICE  METER  — DIFFERENTIAL  GAUGE 
CAPACITIES— DIFFERENTIAL  RANGE— PRESSURE 
CONNECTIONS  OR  TAPS— PRESSURE  LOSS— PULS- 
ATING FLOW— INSTRUCTIONS  FOR  METER  AT- 
TENDANTS AND  TESTING  APPARATUS. 

GENERAL 

In  determining  the  flow  of  fluids  (gases,  vapors,  or  liquids), 
through  pipe  lines  two  general  types  of  meters  are  used,  the 
direct  or  displacement  type  and  the  indirect  or  velocity 
type.  Displacement  meters  are  installed  for  measuring  ordi- 
nary rates  of  flow  under  low  or  high  pressure,  especially  of 
gases  and  vapors.  The  velocity  type  is  generally  used  for 
measurement  in  large  capacity  lines  under  high  pressure. 

The  most  familiar  forms  of  displacement  meters  are  the 
domestic  gas  meter,  the  water  meter  and  the  station  meter. 
The  proportional  meter  also  belongs  to  this  class  although  it 
measures  only  a  definite  percentage  of  the  flow  by  displace- 
ment. The  operation  of  the  direct  type  consists  of  auto- 
matically filling  and  emptying  a  space  of  definite  volume, 
counting  the  number  of  times  the  space  is  filled  and  emptied 
by  means  of  gearing,  indicating  the  result  in  cubic  feet, 
gallons,  pounds,  etc. 

The  velocity  type  includes  the  Pitot  Tube  with  all  of  its 
variations,  and  the  Orifice  Meter,  in  which  the  flow  is  de- 
termined by  the  simple  fact  that  the  volume  flowing  is  equal 

67 


ORIFICE      METER      MEASUREMENT 

to  the  area  of  a  section  multiplied  by  the  rate  of  flow  or 
velocity  through  this  section.  For  example,  if  the  rate  of 
flow  of  a  gas  or  liquid  through  a  pipe  line  whose  area  is  one 
square  foot  is  3000  feet  per  hour  the  volume  passing  any  point 
through  the  line  per  hour  is  equal  to  the  area  of  the  cross 
section  of  the  pipe  (l  sq.  ft.)  multiplied  by  3000  feet  or  3000 
cu.  ft.  per  hour. 

Of  the  velocity  type  the  Orifice  Meter  has  become  the 
most  widely  known  on  account  of  its  adaptability,  simplicity 
and  accuracy.  An  orifice  meter  will  measure  the  flow  of  any 
gas,  vapor  or  liquid  of  fairly  uniform  gravity  at  high  pressure 
or  under  a  vacuum.  In  fact,  they  are  used  successfully  for 
many  kinds  of  gases  and  liquids  such  as  Natural  Gas,  Casing- 
head  Gas,  Manufactured  Gas,  Coke  Oven  Gas,  Pintch  Gas, 
Compressed  Air,  Steam,  Water  and  Oil. 

The  orifice  disc  or  meter  is  simply  a  machined  circular 
plate  one-fourth  inch  in  thickness  having  an  orifice  or  circu- 
lar opening  in  the  center  of  the  plate.  For  cross  section  see 
Fig.  36. 


*e 


Fig.  36— SECTIONAL  VIEW  OF  ORIFICE  DISC 

The  meter  is  installed  by  placing  the  orifice  disc  between 
two  flanges  or  in  a  body  casting  in  a  pipe  line  with  the  center  of 
the  orifice  in  the  center  of  the  pipe,  and  connecting  the  Static 
and  Differential  Pressure  Gauge  with  quarter  inch  pipe  to 
two  taps  in  the  pipe  or  flanges,  one  on  each  side  of  the  orifice 
disc. 

The  accuracy  of  the  meter  depends  only  upon  the  ma- 
chining of  the  orifice  disc  which  can  be  done  easily  with 
extreme  precision.  Any  small  pebbles  or  accumulation  of 

68 


ORIFICE      METER      MEASUREMENT 

dirt  or  rust  in  the  pipe  do  not  produce  an  appreciable  effect 
on  the  results;  whereas,  in  the  other  meters  of  the  velocity 
type  any  obstruction  equivalent  to  only  a  very  small  per- 
centage of  the  area  of  the  pipe  affects  the  accuracy  to  a 
large  extent. 

For  each  installation  the  orifice  in  the  orifice  disc,  when 
placed  in  the  pipe  line,  forms  a  definite  section  of  unchanging 
area,  and  creates  a  definite  difference  between  the  static 
pressure  of  the  fluid  on  the  upstream  side  of  the  orifice,  and 
the  static  pressure  of  the  fluid  on  the  downstream  side  of 
the  orifice,  for  each  velocity  or  rate  of  flow  of  the  fluid,*  at 
the  same  density.  This  difference  in  static  pressures  is 
termed  the  differential  pressure  or  the  "differential."  In 
other  words  the  "differential,"  and  static  pressure,  in  cases 
of  gases  and  vapors,  indicate  the  velocity. 

The  Differential  and  Static  Pressure  Gauge  records  on  a 
chart  the  differential  pressure  existing  between  the  pressure 
connections,  and  the  static  pressure  at  one  of  the  connec- 
tions. These  factors  with  the  known  area  of  the  orifice  enable 
the  operator  to  determine  the  flow  by  multiplying  the  Pres- 
sure Extension  by  the  Hourly  Orifice  Coefficient. 

The  layout  of  an  orifice  meter  installation  may  be  indi- 
cated as  in  Fig  38  where  M  and  F  represent  static  pressure 
gauges  attached  to  the  upstream  connection  at  U  and  down- 
stream at  D  respectively.  The  pressure  connections  are  also 
attached  to  a  U  tube,  upstream  at  H,  and  downstream  at  L. 
When  there  is  no  flow  through  the  line  the  two  gauges  will 
register  the  same,  but  when  a  flow  exists  it  will  be  observed 
that  the  gauge  at  M  will  register  more  than  the  gauge  at  F; 
also  that  the  pressure  at  H  being  greater  than  at  L  will  cause 
the  liquid  in  column  H  to  lower  and  in  column  L  to  raise.  The 
difference  in  the  level  of  surfaces  of  the  liquid  in  the  columns 
being  the  "differential"  h.  If  the  area  of  orifice  is  equal 

*  Throughout  this  volume  the  term  fluids  is  used  to  include  gases,  vapors  and 
liquids  and  the  term  gas  applies  to  any  gas  and  air. 

69 


ORIFICE      METER      MEASUREMENT 


70 


ORIFICE      METER      MEASUREMENT 


to  the  area  of  the  pipe,  the  velocity  through  it  would  be  the 
same  as  in  the  other  adjacent  portions  of  the  pipe. 

If  discs  having  consecutively  decreasing  areas  of  orifices 
are  placed  in  the  same  line,  the  velocity  of  the  fluid  through 
the  orifices  would  be  increased  while  the  static  pressure  at 
the  upstream  connection  would  be  increased  and  the  static 
pressure  at  the  downstream  connection  would  be  decreased. 


Downstream 


Downstream  Static 
Pressure  Connect/on  \^ 


Upstream  Static 
'/Pressure  Connect  ion 


- — 2>irect/on  off/ow 


Fig.  38— DIAGRAM  OF  ORIFICE  METER  INSTALLATION 

The  differential  pressure  between  the  connections  is  the 
pressure  creating  the  flow  between  the  connections.  If  a 
series  of  taps  were  made  in  a  line  of  uniform  size  in  which  a 
fluid  is  flowing,  the  pressures  taken  at  each  of  these  taps 
would  decrease  until  at  the  outlet  it  would  be  zero;  simi- 
larly, if  two  vertical  pipes  were  attached  to  a  line  through 
which  water  is  flowing,  one  on  each  side  of  an  orifice,  it 
would  be  observed  that  the  water  on  the  upstream  side  of 
the  orifice  disc  would  rise  to  a  higher  level  than  that  on  the 
downstream  side  of  the  orifice  disc.  This  difference  in  levels 
is  also  the  pressure  differential,  being  the  same  in  amount 
as  would  be  measured  by  a  differential  gauge,  which  is  a 
modified  form  of  U  tube  using  mercury  as  a  liquid.  The 

71 


ORIFICE      METER      MEASUREMENT 


Fig.  39 


72 


ORIFICE      METER      MEASUREMENT 

difference  in  levels  between  the  surfaces  of  the  mercury  in 
the  columns  of  the  gauge  is  indicated  on  a  chart  by  a  pen 
arm  actuated  by  a  cast  iron  float  moved  by  the  rise  and  fall 
of  the  mercury  in  one  of  the  columns.  See  Fig.  39. 

In  an  actual  installation  the  differential  h  and  static 
pressure,  either  at  M  or  F,  are  usually  recorded  on  the  same 
gauge.  Where  the  pressure  connections  are  made  at  points 
2J/2  diameters  upstream  and  8  diameters  downstream  the 
static  pressure  at  M  is  recorded,  and  where  the  connections 
are  made  at  the  flanges  the  static  pressure  at  F  is  recorded,  as 
the  published  values  of  coefficients  for  these  two  types  of 
connections  were  determined  by  using  the  values  of  the  static 
pressures  obtained  in  this  manner. 

ORIFICES 

Gas  is  being  measured  by  many  types  of  orifices  devel- 
oped by  many  experimenters. 

The  types  generally  used  are;  the  thin  plates  with  the 
cylindrical  hole  which  vary  from  1/32  inch  to  y%  inch  in 
thickness;  plates  of  varying  thickness  from  IJ^  inch  to  J4 
inch,  drawn  down  by  bevelling  at  various  angles  to  a  thin 
edge  at  the  circular  opening  in  the  center  of  the  plate. 

Orifice  plates  are  made  of  such  materials  as  soft  iron, 
coated  with  German  silver  to  prevent  corrosion;  mild  steel 
boilerplates;  case-hardened  or  tempered  steel. 

The  use  of  these  materials  is  due  to  various  theories  as 
to  the  action  of  gas  on  the  disc.  The  non-corrosive  plating 
or  coating  is  used  on  the  theory  that  the  principal  danger 
is  from  change  in  area  of  the  orifice  by  corrosion.  The  use  of 
hardened  steel  is  based  on  the  theory  that  the  principal  danger 
is  a  change  in  area  from  a  scouring  or  sand-blasting  of  the 
hole.  The  mild  steel  plates  are  used  on  the  assumption  that 
neither  of  the  two  effects  mentioned  above  is  a  source  of 
serious  trouble,  but  that  the  important  thing  is  to  be  able 

73 


OR  IFICE      METER      MEASUREMENT 


Fig.  40— THIN  ORIFICE  USED  IN  ORIFICE  FLANGE 


Fig.  41— ONE  TYPE  OF  THIN  PLATE  ORIFICE  USED  IN  ORIFICE 
BODY,  Fig.    1,2 

74 


ORIFICE      METER      MEASUREMENT 


Table  10— ORIFICE  CONSTANTS 


Diameter 
of  Orifice 
Inches 

Square 
of  Diameter 
Inches  2 

Area 
Orifice  Sq.  Ft. 

Volume  in  Cu.  Ft. 
per  hour  for  a 
velocity  of  one 
foot  per  second 

1A 
f8 

n 

.062500 
.  140625 
.250000 
.390625 
.562500 
.  765625 

.000  340  886 
.000  766  993 
.001  363  54 
.002  130  54 
.003  067  97 
.004  175  85 

1.22719 
2  .  76117 
4.90875 
7.66992 
11.0447 
15.0330 

IH 

IX 

iys 

1.000000 
1.265625 
1  .  562500 
1  .  890625 

.005  454  17 
.006  902  93 
.008  522  14 
.010  311  8 

19.6350 
24.8505 
30.6797 
37  .  1224 

ix 

1^8 
1% 

1% 

2.250000 
2.640625 
3  .  062500 
3.515625 

.012  271  9 
.014  402  4 
.016  703  4 
.019  174  8 

44.1788 
51.8487 
60.1322 
69.0293 

2 

2K 
21A 
2s/s 

4.000000 
4  .  515625 
5  .  062500 
5.640625 

.021  816  7 
.024  629  0 
.027  611  7 
.030  764  9 

78.5400 
88.6643 
99.4022 
110.754 

m 
si 

6.250000 
6  .  890625 
7  .  562500 
8  265625 

.034  088  6 
.037  582  6 
.041  247  2 
.045  082  1 

122.719 
135.297 
148.490 
162.296 

3 

3Ji 

sy2 

3% 

9.0000 
10.5625 
12.2500 
14.0625 

.049  087  5 
.057  609  7 
.066  813  6 
.076  699  3 

176.715 
207.395 
240.529 
276.117 

4 

4K 
*H 
4M 

16.0000 
18.0625 
20.2500 
22.5625 

.087  266  7 
.098  515  9 
.110  447 
.123  060 

314.160 
354.657 
397.609 
443.015 

5 

5K 
5K 
5% 

25.0000 
27.5625 
30.2500 
33.0625 

.136  354 
.  150  331 
.164  989 
.  180  328 

490.875 
541.190 
593.959 
649  .  182 

6 

6K 
6H 
6M 

36.0000 
39.0625 
42.2500 
45  .  5625 

.196  350 
.213  054: 
.230  439 
.248  506 

706.860 
766.992 
829  .  579 
894.620 

7 

IK 

7i^ 

7M 
8 

49.0000 
52.5625 
56.2500 
60.0625 
64.0000 

.267  254 
.286  685 
.306  797 
.327  591 
.349  067 

962  .  115 
1032.06 
1104.47 
1179.33 
1256.64 

8K 
83^ 
8% 
9 

68.0625 
72.2500 
76.5625 
81.0000 

.371  224 
.394  064 
.417  585 
.441  788 

1336.41 
1418.63 
1503.30 
1590.44 

75 


ORIFICE      METER      MEASUREMENT 

to  machine  the  orifice  to  an  exact  micrometer  dimension  -so 
that  the  capacity  can  be  determined  by  measurement  of  the 
orifice  and  a  predetermined  coefficient  can  be  used  without 
individual  calibrations  for  each  disc.  The  principle  is  self- 
evident,  that  more  accurate  calibrations  can  be  made  for  a 
determination  for  the  purpose  of  establishing  a  standard  for 
all  meters  than  is  possible  in  individual  calibrations  for  each 


Fig.  42— SECTIONAL  VIEW  OF  AN  ORIFICE  METER  BODY 

individual  meter.  Those  advocating  case-hardened  orifices 
or  orifices  requiring  individual  calibration  believe  that  corro- 
sion and  wear  are  more  dangerous  to  accuracy  than  possible 
variations  in  individual  calibrations. 


76 


ORIFICE      METER      MEASUREMENT 

DETERMINATION  OF  ORIFICE  COEFFICIENTS 

For  Connections  2J/£  Diameters  Upstream  and  8  Diameters 
Downstream 

There  are  several  methods  of  taking  differential  pressures 
on  the  two  sides  of  the  orifices,  each  producing  different 
values  of  the  coefficients. 

It  is  the  intention  of  the  author  to  carefully  explain  the 
complete  methods  used  in  obtaining  the  coefficients  found 
on  Pages  173  to  184.  Due  credit  should  be  given  not  only 
to  the  Wichita  Pipe  Line  Co.  of  Bartlesville,  Okla.,  but  to 
A.  J.  Discher,  formerly  General  Manager,  F.  P.  Fisher, 
formerly  Assistant  General  Manager,  and  to  E.  O.  Hick- 
stein,  who  carried  out  the  actual  tests. 

Primarily,  it  might  be  said  that  the  work  was  started  by 
the  Wichita  Pipe  Line  Co.,  whose  permission  was  obtained 
for  the  publication  of  the  coefficients  in  the  first  edition  of 
this  book.  Other  companies  have  since  checked  these  co- 
efficients and  very  little  necessity  for  revision  has  been 
found. 

While  Mr.  E.  O.  Hickstein  was  the  engineer  in  charge  of 
all  tests,  he  was  ably  assisted  by  other  engineers  in  the  work. 
Every  facility  was  given  the  corps  of  engineers  in  the  above 
work.  Such  equipment  as  artificial  gas  holders  and  high 
pressure  pipe  lines  of  several  miles  in  length  were  used. 

The  work  was  not  accomplished  in  a  few  weeks  or 
months,  but  covered  a  period  of  several  years,  and  not 
until  the  coefficients  had  been  in  use  for  two  or  three  years 
were  they  published. 

Later  tests  were  made  using  a  2200  cubic  foot  holder 
enclosed  within  a  building.  These  were  known  as  the  Erie 
tests,  and  were  made  at  the  Plant  of  the  Metric  Metal  Works. 
The  author  was  present  during  these  tests  which  required 
about  one  month's  time. 

77 


ORIFICE      METER      MEASUREMENT 

The  work  was  done  in  1913  and  cannot  be  said  to  be 
completed  at  this  writing.  However,  in  1915  sufficient  work 
had  been  done  to  warrant  placing  the  coefficients  before 
other  gas  companies  for  their  use  as  well  as  criticism. 

JOPLIN  HOLDER  TESTS* 

"The  discs  tested  by  the  method  to  be  described  are 
machined  out  of .  quarter-inch  boiler  plate  or  tool  steel.  The 
edge  of  the  orifice  proper  is  flat  for  A  in.  to  i  in.  and  bev- 
elled at  45  deg.  for  the  remainder  of  the  thickness  of  the  plate. 

The  ordinary  practice  in  orifice  meter  installations  is  to 
have  the  gauge  line  connections  right  at  the  flange,  that  is, 
the  inlet  and  the  outlet  pressures  are  taken  within  an  inch 
or  two  of  the  orifice  disc,  through  holes  drilled  into  the 
companion  flanges.  In  this  particular,  the  meters  of  the 
type  tested  by  the  author  show  a  departure  from  the  com- 
mon practice.  In  the  meters  tested,  the  high  pressure  con- 
nection was  two  and  a  half  times  the  diameter  of  the  pipe 
line  ahead  of  the  orifice  disc,  and  the  low  pressure  connection 
was  eight  times  the  diameter  of  the  pipe  line  behind  the 
disc.  This  means  that  in  an  orifice  meter  installation  on  a 
10  in.  line,  for  example,  the  high  pressure  connection  is  25  in. 
in  front  of  the  disc,  and  the  low  pressure  connection  80  in. 
behind  it,  regardless  of  the  size  of. the  orifice  in  the  line. 

It  was  found  by  experiments  made  at  Charlottenburg 
some  eight  years  ago  (1907),  that,  for  any  flow  through  an 
orifice  disc  not  giving  an  excessive  drop  in  pressure,  pressure 
connections  at  just  the  distances  mentioned  above  would  give 
a  smaller  pressure  drop  across  the  disc  than  would  con- 
nections placed  at  any  nearer  position  to  the  disc.  There 
can  hardly  be  any  doubt  but  that  the  inserting  of  an  orifice 
disc  in  a  pipe  line  would  cause  eddies,  and  while  there  is  no 

*Extracts  from  "The  Flow  of  Air  through  Thin  Plate  Orifices,"  by  E.  O.  Hick- 
stein,  Jun.  Am.  Soc.  M.  E. — Presented  at  the  Annual  Meeting  of  the  American 
Society  of  Mechanical  Engineers,  Dec.  7-10,  1915. 

78 


ORIFICE      METER      MEASUREMENT 

evidence  to  show  that  the  presence  of  eddies  would  affect  the 
accuracy  of  any  measurement  through  the  disc,  it  was  thought 
best  to  eliminate  this  source  of  possible  uncertainty. 

Derivation  of  Orifice  Meter  Formulae  for  Flow  of  Air* 
The  fundamental  formula  for  flow  through  an  orifice  is 

r=c,v~2~Tff [i] 

where  V  =  velocity  of  flow  through  the  orifice,  ft.  per  sec. 

Cv  =  so-called  "velocity  coefficient,"  varying  with  the 
size  and  shape  of  the  disc.  This  constant  is  also 
known  sometimes  as  the  "efficiency,"  though  this 
term  is  misleading. 

g  =  acceleration  due  to  gravity,  ft.  per  sec.,  per  sec. 
H  =  drop  in  pressure  through  the  orifice  disc,  expressed 
in  feet  of  head  of  the  fluid  flowing,  at  temperature 
and  pressure  conditions  of  flow. 

In  this  fundamental  formula,  the  differential  drop  across 
the  orifice  is  given  in  terms  of  feet  head  of  fluid.  The  differ- 
ential pressure  gauges  used  in  commercial  meter  installations 
are  nearly  all  graduated  to  read  in  inches  of  water  drop  in 
pressure.  It  is  necessary,  therefore,  to  derive  from  the  funda- 
mental formula  an  expression  in  which  the  drop  is  in  terms 
of  inches  of  water.  This  can  readily  be  done,  as  follows: 

Assuming  air  as  the  flowing  fluid,  the  fundamental 
formula  [1]  can  be  written 

-    ^^-..JTT*..  ..[2] 


where  Q\=  volume  of  fluid  (air  in  this  case)  flowing  per 
15  min.,  in  cubic  feet  at  pressure  and  temperature 
P  and  T  respectively  (the  conditions  at  inlet  of 
orifice) 

d  =  diameter  of  orifice,  in. 

Cv,  g  and  H  as  in  the  fundamental  formula  [1]. 

"The  subscripts  in  this  article  have  been  changed  by  the  author  to  conform  to 
the  remainder  of  the  book. 

79 


ORIFICE      METER      MEASUREMENT 

To  reduce  the  value  Qi,  which  expresses  volume  at  tem- 
perature and  pressure  conditions  of  flow,  to  Q,  the  volume 
at  the  standard  conditions  of  temperature  and  pressure 
(call  Tb  and  Pb  the  standard  conditions) ,  it  is  only  necessary 
to  apply  the  perfect  gas  law.  This  is  done  by  multiplying 
the  right-hand  side  of  equation  [2]  by  PTb/PbT. 

The  drop  in  head,  H,  now  expressed  in  feet  of  fluid  at 
P  and  T,  must  be  reduced  to  inches  of  water,  as  explained 
above.  Kent  gives  1  ft.  of  air  at  32  deg.  fahr.  as  equal  to 
0.015534  in.  head  of  water  at  62  deg.  From  this,  one  foot 
head  of  air  at  P  and  T  is  equal  to  (0.015534  P  492)  -r-  (14.7  X 
T)  inches  head  of  water  at  62  deg.  Formula  [2]  can  now  be 
written : 


0_c,w»~  ^  *~  °  r      I      2gA.14.7  T 

4X144  PbT     ;V  0.015534  X492XP-" 
and  then  simplified  to 

^  ~  jPfr    *  \  ~~T ^ 

Formula  [41  is  the  general  formula  for  calculating  the 
flow  of  air  through  an  orifice  disc.  A  further  simplification 
of  this  formula  is  practicable,  however,  for  commercial  pur- 
poses. As  the  temperature  of  the  flowing  gas  is  not  usually 
measured,  an  average  value  is  assumed.  This  is  taken  in 
Oklahoma  as  60  deg.  fahr.  The  pressure  and  temperature 
standards  are  definite,  being  usually  fixed  by  contract.  All 
these  values,  together  with  d,  the  diameter  of  the  orifice,  can 
be  assembled  into  one  constant,  which  reduces  formula  [4]  to 

Q  =  Ca  V  h  P [5] 

where  Cais  the  so-called  "air  constant,"  found  experimentally. 

Orifice  Meter  Formulae  for  Gas 

The  orifice  meter  formulae  for  flowing  gas  are  derived 
by  the  same  steps  as  those  for  flowing  air.  In  the  reduction 
of  H  (the  differential  of  the  fundamental  formula  expressed 

80 


ORIFICE      METER      MEASUREMENT 

in  feet  head  of  the  fluid)  to  h  (the  differential  in  inches  of 
water)  the  density  of  the  gas  must  be  considered.  If  the 
specific  gravity  of  the  gas  be  taken  as  G,  where  air  equals 
unity,  the  general  formula  for  the  flow  of  gas  through  an 
orifice  meter  becomes 


G  T 
This  formula  corresponds  with  formula  [4]  for  flowing  air. 

The  simplified  commercial  formula  for  a  gas  flow  becomes 

e=7^VT^0rcs  JTT ,...,,..[7] 

where  Cg  is  the  so-called  "gas  coefficient,"  the  meaning  of 
which  will  be  explained.  This  formula  corresponds  with 
formula  [5]  for  flowing  air. 

Formula  [7]  is  the  formula  actually  used  in  commercial 
measurement.  The  values  of  P  and  h  are  shown  by  the 
recording  pressure  and  differential  pressure  gauges,  and  Cg  is 
mathematically  derived  from  the  constant  of  the  disc  as 
found  by  experiment.  From  the  two  readings  and  the  gas 
coefficient,  the  delivery  through  the  meter  can  be  calculated. 

Relationship  Between  the  Constants,  Cv,  Ca  and  Cg 

As  a  rule,  the  theoretical  velocity  coefficient,  Cv,  is  not 
used  in  calculating  deliveries  through  an  orifice.  Its  useful- 
ness lies  principally  in  the  mathematical  analysis  of  the 
formulae  and  for  purposes  of  comparing  experimental  data 
of  tests  made  under  widely  differing  conditions. 

Ca,  the  air  constant,  and  Cg,  the  gas  coefficient,  are  the 
quantities  that  are  used  commercially.  The  relation  be- 
tween these  two,  as  can  be  seen  by  comparing  formulae  [5] 
and  [7] ,  is  expressed  by  the  equation 

Cg=-^=.  ..[8] 

VG 

81 


ORIFICE      METER      MEASUREMENT 

Ca,  the  air  constant,  is  the  value  that  is  experimentally 
found,  and  does  not  vary  for  any  disc,  unless  the  assumed 
standards  are  changed.  The  gas  coefficient,  on  the  other 
hand,  being  a  function  of  the  gravity  of  the  flowing  gas,  will 
vary,  and  the  gas  coefficients  of  identical  discs  would  be 
different  if  the  discs  were  passing  gases  of  different  gravities. 
Orifice  disc  calibration  tests  are  therefore  usually  figured  for 
C0,  the  air  constant,  and  this  is  the  value  that  is  recorded. 
Whenever  a  disc  is  put  in  line  at  a  measuring  station,  the 
gravity  of  the  gas  to  be  measured  is  found  by  a  test,  and  the 
proper  gas  coefficient  calculated. 

The  relation  between  Cv  and  Ca  is  found  by  equating 
the  right-hand  sides  of  formulae  [4]  and  [5],  and  can  be 
expressed  as  r 

C,  =  11.55-^ [9] 

General  Outline  of  the  Joplin  Tests 

The  tests  on  orifice  meter  discs  to  be  described  in  this 
paper  were  carried  out  at  Joplin,  Mo.  The  discs  were  cali- 
brated against  the  displacement  of  air  from  an  old  artificial 
gas  holder  at  that  place.  The  holder  was  a  two-lift  holder, 
water  sealed  and  of  250,000  cu.  ft.  nominal  capacity.  Roughly 
speaking,  its  dimensions  were  90  ft.  in  diameter  by  40  ft. 
total  height.  The  lower  lift  only  was  used  in  the  te,sts;  this 
lift  has  a  capacity  of  110,000  cu.  ft.  The  reason  for  using 
only  the  lower  lift  was  the  change  in  pressure  of  the  air  in  the 
holder,  as  one  lift  seated  on  the  bottom. 

Of  the  several  original  outlets  from  the  holder,  all  but 
one  were  securely  blanked.  The  remaining  12  in.  outlet  was 
led  into  a  long  building,  and  connected  to  a  straight  run  of 
some  40  ft.  of  pipe,  near  the  center  of  which  was  the  orifice 
flange.  The  air  passing  out  of  the  holder  went  through  the 
orifice  disc,  and  discharged  into  the  atmosphere  perhaps  20  ft. 
beyond.  A  motor  driven  blower  was  used  to  fill  the  holder 
with  air  previous  to  each  test. 

82 


ORIFICE      METER      MEASUREMENT 

LEAKAGE  TESTS  ON  HOLDER. — The  first  tests  made  were 
to  determine  the  rate  of  leakage  from  the  holder.  In  order 
to  obtain  a  fair  average,  a  number  of  such  tests  were  run  at 
the  start,  with  the  holder  at  varying  heights.  Leakage  tests 
were  also  run  at  intervals  throughout  the  whole  work,  to 
make  sure  that  the  leakage  figure  first  obtained  had  not 
materially  changed. 

The  first  leakage  tests  (run  during  August,  1913)  were 
unsatisfactory  on  account  of  the  large  difference  between 
temperature  conditions  at  the  start  and  finish  of  test.  To 
avoid  this  difficulty,  tests  of  24  hours  duration,  starting  at 
about  midnight,  were  made,  and  better  results  obtained. 
The  average  of  three  long  leakage  tests  showed  103  cu.  ft. 
leakage  per  hr.  The  correction  used  in  all  the  Joplin  tests 
was  taken  as  100  cu.  ft.  per  hr.  The  result  of  later  leakage 
tests  showed  practically  the  same  leakage  as  the  above 
average,  the  highest  value  in  any  24  hr.  test  being  115  cu.  ft. 
per  hr. 

CHANGES  OF  VOLUME  IN  HOLDER  WITH  TEMPERATURE 
VARIATION. — During  the  leakage  tests,  it  was  noticed  that 
the  rise  and  fall  of  the  holder  with  temperature  changes  was 
a  greater  factor  than  had  been  anticipated.  A  4  ft.  rise  from 
midnight  to  noon  was  not  uncommon  during  the  hot  weather. 
It  was  necessary,  therefore,  to  ascertain  very  accurately  the 
proper  correction  to  apply  for  temperature  changes  taking 
place  during  a  test. 

Table  11  shows  observations  and  calculated  results  made 
in  a  test  run  for  this  purpose.  The  holder  was  filled  to  about 
three  quarters  capacity  and  allowed  to  stand,  hourly  read- 
ings being  taken  of  all  quantities  involved.  The  so-called 
"top"  temperature  is  the  reading  found  by  lowering  a  ther- 
mometer 2  ft.  or  so  into  the  holder  through  a  bolt  hole  on  top. 

From  the  data  the  net  change  in  volume  due  to  tem- 
perature variation  for  each  hourly  period  was  calculated.  It 
was  found  that  the  changes  in  volume  as  observed  were 

83 


ORIFICE      METER      MEASUREMENT 


Table  11— Readings  and  Calculated  Results  of  First  24 
Hours  Test  on  Gas  Holder  for  Investigating  Variation 
of  Volume  of  Air  in  Holder  with  Temperature  Change. 


Change  of  Volume  of 

Air  in  Holder  Cor- 

rected for  Level  of 

Calculated 

Same 

Time 

Temperatures 

Water   Seal  and  for 
Leakage 
In.  Height 

Calcu- 
lated 
"Com- 
bined" 

Theoret- 
ical Change 
of  Volume 
from 

Values 
Corrected 
for 
Calculated 

Temp. 

Beginning 

Lag  of 

81  £      ' 

During 

From 

of  Test 

%  m. 

Atmos. 

"Top" 

Previous 

Beginnine 

at  Start 

Hour 

of  Test 

6  p.  m. 

96 

103 

98% 

-8K 

7  p.  m. 

93 

97 

—  STF 

—  &TS 

94% 

—  6% 

—14% 

8  p.  m. 

90 

91 

-sit 

—17% 

90% 

—  11% 

—20% 

9  p.  m. 

88 

88 

-4% 

-21% 

88 

—15% 

-23% 

10  p.  m. 

87% 

86 

—2% 

—24% 

87 

—16% 

-24% 

11  p.  m. 

86 

86 

—  1% 

—  25M 

86 

—  17% 

—25% 

12  night 

85 

85 

—  IIT 

-26H 

85 

—18% 

—27% 

1  a.  m. 

84 

84 

—  1M 

-27H 

84 

—20% 

-28% 

2  a.  m. 

82 

83 

—  1% 

—29^ 

82% 

—21% 

—30 

3  a.  m. 

81 

82 

-1% 

-30^ 

81% 

—23 

—  31M 

4  a.  m. 

80 

81 

—\l/i 

—  31r6 

80% 

—24% 

-32% 

5  a.  m. 

79% 

80 

-1% 

-32H 

79% 

—25 

—  33^ 

6  a.  m. 

78% 

80 

-  M 

-33^ 

79 

—  25M 

—34 

7  a.  m. 

80 

86 

5% 

—  27yf 

82 

—27% 

—30% 

8  a.  m. 

85% 

100 

7% 

—  20]I 

90% 

—10% 

—19 

9  a.  m. 

87% 

108 

m 

94% 

—  5 

—  13M 

10  a.  m. 

92 

118 

7_^ 

—  5% 

101 

4% 

-3% 

lla.m. 

95 

122 

7% 

1% 

104 

9% 

% 

12  noon 

96 

131 

5% 

6% 

108 

16% 

8% 

1  p.  m. 

98 

132 

2% 

9M 

109% 

19% 

10% 

2  p.  m. 

100% 

131% 

1 

10/4 

111 

21% 

13% 

3  p.  m. 

100% 

129 

2;nr 

12re 

110 

20 

11% 

4  p.  m. 

98% 

126 

—  2jf 

9% 

107% 

15% 

7% 

5  p.  m. 

97 

117 

—  2/4 

6¥ 

104 

9K 

1M 

6  p.  m. 

94% 

109 

-4ft 

99% 

2 

_** 

Height  of  top  of  holder,  at  start,  above  water  in  seal,  421  in. 
Date  of  test,  August  8-9,  1913. 

84 


ORIFICE      METER      MEASUREMENT 

always  greater  than  a  calculation  based  on  the  ratio  of  abso- 
lute temperatures  alone  would  give.  After  some  little  study 
and  debating,  it  was  decided  that  this  was  due  to  the  presence 
of  aqueous  vapor  in  the  holder.  This  point  has  always 
appeared  especially  interesting,  and  therefore  deserves  fur- 
ther analysis  here. 


LU.V 

29.4 
Z9.Z 

290 
28.8 
28.6 
28.4 
28.2 
28.0 
278 
216 
27.4 
27.2 
27.0 
268 

-o-~ 

"•     — 

-o  — 

1~Q--~, 

, 

-<^ 

"•»•>, 

^ 

\ 

X 

\ 

\ 

\ 

\ 

fapor  Tension  af  the  differen 
Temperatures,  deducted  fron 
Total  Holder  Pressure. 
Circles  indicate  Points  fauna 
by  Computation 

/ 

\ 

7 

\ 

r 

\ 

\ 

\ 

\ 

* 

""TO         30         40           50          60          70          80         90          100          110          12 

Fig. 


Temperatura  of  Holder  Air,Deg  Fahr. 

43— CALCULATED  "GAS  PRESSURE"  IN  HOLDER  WITH  VARYING 
TEMPERATURE 


That  saturated  water  vapor  was  present  in  the  holder 
air  is  evident.  By  Dalton's  Law,  it  is  correct  to  assume  that 
the  pressure  inside  the  holder  is  made  up  of  two  distinct 
quantities  (a)  the  tension  of  the  saturated  aqueous  vapor, 
(b)  the  pressure  of  the  air  in  the  holder.  The  sum  of  these 
two  component  pressures,  expressed  as  absolute,  will  be  the 
barometer  reading  plus  the  reading  of  a  U  tube  connected 
up  to  the  holder  pressure.  Therefore,  for  a  constant  baro- 

85 


ORIFICE      METER      MEASUREMENT 

meter,  the  total  pressure  of  the  holder  will  not  change.  If, 
however,  the  temperature  should  rise  while  the  barometer 
remains  constant,  the  tension  of  the  saturated  vapor  will 
increase,  and  the  second  component  of  the  total  pressure, 
the  pressure  of  the  air  (which  will  be  called  the  "gas  pressure" 
in  this  connection)  must  be  correspondingly  decreased.  With 
varying  barometer  readings,  this  change  in  value  of  each 
component  pressure  will  be  different.  However,  a  very  close 
approximation  can  be  had  by  basing  all  corrections  on  the 
average  barometric  reading  at  Joplin,  viz.,  29.3  in. 


1.180 
1.160 
1.140 
1.120 
I.KX) 
1.080 
1.060 
LWO 
1.020 
1.000 
0.980 
0.960 
0540 
0.9ZO 
0300, 

i 

/ 

i 
Circles  indicate  Points  found  by  Computation. 
Volume  at  70  Deg.Fanr  assumed  as  Unity  (Line  A) 
Volume  Variation  by"Boy!es"Lan  shown  by  Curve  & 

i 

7J 

/ 

/ 

/ 

,-- 

/ 

5 

^ 

/ 

^^ 

,** 

/ 

j? 

^^ 

/ 

^r"*' 

A 

*'l 

r 

^" 

^ 

r 

^*- 

/ 

s 

^^' 

* 

Lx" 

ys 

ft 

r  30      40       50      60       TO       80      90       100      110      12 
Temperature  of  Air,Deg.Fahr. 

Fig.  44— CALCULATED  VARIATION  IN  VOLUME  OF  AIR  ENCLOSED  IN 
HOLDER  OVER  WATER,  WITH  CHANGE  OF  TEMPERATURE 


For  any  temperature,  the  second  component  of  the 
total  holder  pressure — the  gas  pressure — can  be  found  by 
subtracting  from  the  total  holder  pressure  the  vapor  tension 
for  the  temperature.  The  total  pressure  is  the  assumed 

86 


ORIFICE      METER      MEASUREMENT 

barometric  reading,  29.3  in.,  plus  the  observed  pressure  of 
the  holder,  4.60  in.  of  water.  The  vapor  tension  for  varying 
temperatures  can  be  found  in  any  handbook.  Fig.  43  shows 
the  variation  of  the  gas  pressure  in  the  holder  for  temperature 
changes.  The  circles  indicate  points  found  by  computation, 
and  through  these  the  curve  is  drawn. 


15 
10 
5 
0 
-5 
HO 

-20 
.-25 

-30 
-35 


Points  joined  by  

Solid  Lines  indicate 
Actual  Rise  and.  faJf. 

Points  joined 
by  Dotted 'Lines 
indicate  Theoretical 
Rise  and  fall 


<b     ft     10    12     Z     4     6     8    10    12     2     4-     6 

Night  Noon 

August  6^,  1913  August  9ib,  1913 


Pig.  45— ACTUAL  AND    THEORETICAL     RISE   AND  FALL  OF  HOLDER 
UNDER    TEMPERATURE   CHANGES.     FIRST  24  HR.    TEST. 


87 


ORIFICE      METER      MEASUREMENT 


Charles'  law  states  that  the  ratio  Pv/T  is  constant  fora 
perfect  gas.  Under  such  small  changes  of  pressure  and  tem- 
perature, air  can  be  assumed  a  perfect  gas.  The  value  of  the 
pressure  corresponding  with  the  temperature  being  known 
from  Fig.  43,  the  volume  can  be  found  by  calling  the  volume 
at  any  assumed  standard  temperature  unity.  In  these  cal- 
culations, the  volume  at  70  deg.  fahr.  is  taken  as  unity.  The 
full  curve  of  Fig.  44  is  the  final  result.  Dotted  in,  for  pur- 
poses of  comparison,  is  a  curve  showing  the  Boyle's  law 


Pointsjoine, 
Lines  indicate  Actuaf 
Rise  and  Faff.  Points 
joined  by  Doffed  Lines 
indicate  Theoretlc&f 
Rise  and  Fall 


& 


246 


10    12     E     4     &     8     10    12 

Noon  Night 

Aucjust  !&*&,  1913.  August  19^,  1913 

Fig.  46— ACTUAL  AND   THEORETICAL  RISE  AND  FALL  OF    HOLDER, 
UNDER  TEMPERATURE  CHANGES.     SECOND  24  HR.  TEST. 

88 


ORIFICE      METER      MEASUREMENT 

variation  for  constant  pressure.  It  can  be  seen  at  a  glance 
that  the  volume  variation  under  temperature  changes,  as 
observed  at  Joplin,  is  considerably  more  than  it  would  be  in 
the  absence  of  the  water  vapor. 

To  go  back  to  the  test  made  on  the  holder  to  study  the 
correction  to  be  applied  for  varying  temperatures,  taking 
account  of  the  effect  of  the  vapor  tension,  as  just  explained, 
it  was  found  in  the  study  of  the  volume  variation  with  tem- 
perature that  the  observed  rise  and  fall  of  the  holder  during 
the  test  corresponded  with  a  temperature  change  equal  to 
the  sum  of  two-thirds  the  atmospheric  temperature,  plus  one- 
third  the  "top"  temperature.  This  simply  means,  of  course, 
that  the  average  temperature  of  the  holder  air  is  that  com- 
bination of  the  two  observed  temperatures. 

Fig.  45  shows  a  test  of  the  correctness  of  this  average 
temperature  of  the  holder  air.  The  dotted  curve  shows  the 
computed  theoretical  rise  and  fall  of  the  holder,  using  the 
temperature  correction  just  described,  and  based  on  the  so- 
called  "combined"  temperature.  The  heavy  curve  shows  the 
actual  rise  and  fall  observed.  These  two  curves  follow  each 
other  fairly  well,  except  for  a  lag  during  the  middle  of  the 
day.  They  bear  the  closest  relation  during  the  period  be- 
tween 9  P.  M.  and  6  A.  M.,  when  the  effect  of  the  sun  shining 
down  on  the  black  holder  top  is  not  present.  During  the 
afternoon  it  is  evident  that  the  "top"  temperature  has  a 
greater  proportionate  effect  on  the  average  temperature  of 
the  air  in  the  holder  than  the  "combined"  temperature  allows. 

Fig.  46  shows  curves  of  a  similar  nature  for  a  second  run 
made  to  check  the  results  of  the  first  run.  The  actual  and 
theoretical  rise  and  fall  of  the  holder,  plotted  on  the  same 
scale  over  each  other,  again  show  very  good  agreement,  par- 
ticularly during  the  night.  The  lag  during  the  hottest  part 
of  the  day  is  again  shown,  in  somewhat  better  shape,  due  to 
the  fact  that  this  second  test  was  started  at  6  A.  M.,  while  the 
first  started  at  6  p.  M. 

89 


ORIFICE      METER      MEASUREMENT 


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90 


ORIFICE      METER      MEASUREMENT 

Description  of  Procedure  During  Orifice  Tests 

Table  12  shows  a  sample  page  of  the  observations  and 
calculated  results  of  one  orifice  test.  These  tests  were  made 
with  a  flying  start,  that  is,  the  air  was  started  discharging 
through  the  meter  orifice  several  minutes  before  the  first 
tank  level  reading  was  taken.  The  final  tank  level  reading 
was  taken  under  similar  conditions.  Half -hourly  readings  of 
atmospheric  temperature,  "top"  temperature,  tank  level, 
water  level  in  seal,  differential  drop  in  inches  of  water  across 
orifice  disc,  and  the  temperature  of  the  discharged  -air  were 
taken.  To  facilitate  calculation,  the  tank  level  reading  was 
taken  by  a  gauge  stick,  marked  off  in  cubic  feet  displacement. 
The  exact  diameter  of  the  lower  lift  was  found,  and  from 
this  it  was  computed  that  a  displacement  of  100  cu.  ft.  cor- 
responded with  a  holder  drop  of  0.1835  in.  This  100  ft. 
graduation  was  the  smallest  on  the  gauge  stick.  The  space 
could  readily  be  divided  visually  into  quarters,  so  the  con- 
tent of  the  holder  at  any  moment  could  be  read  to  the 
nearest  25  cu.  ft.  Differences  between  two  consecutive  half- 
hourly  tank  level  readings  would  therefore  give  the  uncor- 
rected  (or  apparent)  quantity  of  air  passing  out  in  that 
period.  Preliminary  corrections  have  to  be  applied  to  this 
value  as  follows:  (1)  holder  leakage,  at  the  rate  of  100  cu.  ft. 
per  hr.,  (2)  variation  of  the  water  level  in  seal,  due  to  leakage 
out,  evaporation,  or  pumping  in  of  fresh  water,  (3)  tem- 
perature change  during  test.  With  these  corrections  applied, 
the  correct  quantity  of  air  passing  through  the  orifice  is 
obtained.  This  quantity,  however,  is  expressed  at  holder 
pressure,  and  at  some  definite  temperature,  varying  from 
day  to  day,  i.  e.,  the  "combined"  temperature.  A  reduction 
is  necessary  in  order  that  the  quantity  of  air  passing  through 
the  orifice  may  be  expressed  in  cubic  feet  at  standard  con- 
ditions of  pressure  and  temperature,  (29.4  in.  of  mercury  or 
14.41  Ib.  per  sq.  in.,  and  60  deg.  fahr.). 

91 


ORIFICE      METER      MEASUREMENT 


Table  13— Summary  of  Holder  Tests  on  8  in.  Orifice  Meters 


Test 
No. 

No.  of 
Meter 
Disc 

Date  of 
Test  and 
Duration 
in  Hr. 

Avg.Corr. 
Rate 
Cu.  ft. 
in  30  min. 

U-Tube 
Read- 
ing, 
In. 
Water 

Baro- 
meter 
In.  Mer 
cury 

Observed  Temp. 

Calc. 
Ca 

Flow 

"Com- 
bined" 

201 

8401 

Sept.  25  iy2 

15,503 

4.07 

29.3 

58 

52 

1.035 

202 

8501 

26  2 

25,361 

3.31 

29.3 

62 

56 

1.868 

203 

8301 

26  3 

8,178 

4.415 

29.3 

58 

54 

0.522 

204 

8351 

27  3 

11,671 

4.26 

29.3 

62 

60 

0.752 

205 

8451 

27  3 

20,223 

3.82 

29.3 

62 

60 

1.375 

206 

8451 

28  2 

20,589 

3.79 

29.2 

64 

61 

1.409 

207 

8351 

28  3 

11,668 

4.33 

29.2 

61^ 

60 

0.747 

208 

8401 

28  2y2 

15,796 

4.11 

29.2 

61 

58 

1.041 

209 

8351 

30  2y2 

11,850 

4.31 

29.3 

66 

62 

0.759 

210 

8451 

30  2 

20,421 

3.83 

29.3 

64 

59 

1.394 

211 

8501 

Oct.    2  iy2 

26,647 

3.36 

29.3 

70 

67 

1.914 

212 

8501 

2  iy2 

26,187 

3.40 

29.3 

Qiy2 

63 

1.883 

213 

8401 

2  2% 

15,839 

4.14 

29.3 

65 

60^ 

1.038 

214 

8301 

3  2y2 

6,124 

2.355 

29.3 

70 

69 

0.527 

215 

8301 

4  5>i 

8,496 

4.41 

29.2 

70 

iQy2 

0.532 

216 

8201 

6  4  }/2 

3,579 

4.52 

29.2 

68 

65 

0.2234 

217 

8201 

•     7  4^| 

2,575 

2.37 

29.3 

69 

65 

0.2217 

218 

8452 

Nov.     3  2 

18,989 

3.37 

29.4 

58 

55 

1.387 

219 

8452 

3  2)4 

18,772 

3.42 

29.4 

57 

54 

1.358 

220 

8452 

4  2 

18,970 

3.44 

29.5 

57 

52 

1.372 

221 

8452 

4  2 

18,791 

3.44 

29.5 

55 

49 

1.361 

222 

8502 

5  2 

23,099 

2.81 

29.45 

57 

52 

1.841 

223 

8502 

5  iy2 

23,215 

2.82 

29.45 

56 

50 

1.853 

224 

8502 

5  11A 

23,375 

2.80 

29.45 

55 

50 

1.879 

225 

8201 

6  5 

3,641 

4.52 

29.3 

60 

59 

0.2274 

226 

8301 

11  3^ 

8,166 

4.33 

29.35 

59^ 

5sy2 

0.521 

227 

8301 

12  sy2 

8,248 

4.34 

29.35 

64 

65 

0.520 

228 

8502 

13  2 

23,485 

2.80 

29.4 

63 

64^ 

1.852 

229 

8201 

14  5 

3,566 

4.53 

29.45 

64^ 

64^ 

0.2248 

230 

8201 

15  4 

3,560 

4.585 

29.3 

54 

49 

0.2242 

231 

8352 

Dec.      5  3 

11,257 

4.10 

29.4 

59 

56 

0.742 

232 

8601 

6  \y2 

31,267 

1.70 

29.2 

55^ 

46 

3.273 

233 

8352 

5  4 

11,241 

4.18 

29.1 

55^ 

48 

0.746 

92 


ORIFICE      METER      MEASUREMENT 


Table  14— Summary  of  Holder  Tests  on  8  in.  Orifice  Meters 


Test 
No. 

No.  of 
Meter 
Disc 

Date  of 
Test  and 
Duration 
in  Hr. 

Avg.Corr. 
Rate 
Cu.  ft. 
in  30  min. 

U-Tube 
Read- 
ing, 
In. 
Water 

Baro- 
meter 
In.Mer 
cury 

Observed  Temp. 

Calc. 
Ca 

Flow 

"Com- 
bined" 

234 

8601 

7  iy2 

30,478 

1.65 

29.5 

51 

33 

3.293 

235 

8352 

6  3l/2 

11,310 

4.09 

29.2 

55 

46 

0.762 

236 

8601 

7  11A 

30,463 

1.65 

29.5 

51 

31 

3.306 

237 

8353 

5  4^ 

11,161 

4.08 

29.4 

59y2 

56 

0.738 

238 

8502 

7  11A 

22,758 

2.90 

29.5 

50 

30 

1.866 

239 

8601 

30  iy2 

36,548 

2.355 

29.3 

47 

3234 

3.305 

240 

8551 

30  iy2 

31,023 

2.99 

39.3 

48 

33 

2.487 

241 

8551 

31  iy2 

30,942 

3.00 

29.2 

50^ 

37 

2.467 

242 

8571 

31  iy2 

33,982 

2.665 

29.2 

49 

37 

2.871 

243 

8571 

Jan.       1  iy2 

29,408 

1.965 

29.0 

53^ 

46^ 

2.865 

244 

8601 

i  iy2 

31,093 

1.64 

29.0 

53 

45 

3.32,5 

245 

8551 

1    1^2 

27,337 

2.30 

29.0 

52 

4034 

2.485 

246 

8352 

2  zy2 

10,969 

4.13 

29.3 

48^ 

30 

0.752 

247 

8352 

2  zy2 

11,148 

4.31 

29.3 

48 

27^ 

0.752 

248 

8551 

3  iy2 

26,775 

2.285 

29.3 

48^ 

3134 

2.468 

249 

8601 

3  iy2 

30,503 

1.615 

29.3 

49^ 

32 

3.344 

250 

8571 

3  iy2 

28,495 

1.96 

29.3 

48^ 

28!4 

2.853 

251 

8521 

Feb.    16  iy2 

28,108 

3.13 

29.4 

49 

42 

2.163 

252 

8251 

18  3 

5,684 

4.62 

29.1 

47^2 

35^ 

0.3653 

253 

8251 

19  zy2 

5,536 

4.51 

29.3 

49 

35 

0.3599 

254 

8521 

19  iy2 

28,075 

3.22 

29.3 

47^ 

35 

2.162 

255 

8151 

20  9 

1,877 

4.63 

29.4 

5234 

31 

0.1216 

256 

8151 

21  5y2 

2,144 

4.63 

29.7 

56 

49 

0.1338 

257 

8151 

23  9 

1,802 

4.61 

29.6 

46 

12^ 

0.1196 

258 

8305 

Mar.     4  3 

8,101 

4.49 

29.4 

5234 

36 

0.5275 

259 

8506 

6  iy2 

23,425 

3.00 

29.5 

4934 

35^ 

1.865 

260 

8506 

9  iy2 

23,617 

2.96 

29.4 

5234 

44 

1.867 

261 

8473 

25  iy2 

22,375 

3.30 

29.35 

5sy2 

64^ 

1.615 

262 

8474 

25  iy2 

21,985 

3.28 

29.35 

59 

6434 

1.595 

263 

8473 

25  iy2 

22,162 

3.28 

29.4 

59 

Q21A 

1.615 

ORIFICE      METER      MEASUREMENT 


Table  15 — Summary  of  Holder  Tests  on  8  in.  Orifice  Meters 


Test 
No. 

No.  of 
Meter 

Date  of 
Test  and 
Duration 

Avg.Corr. 
Rate 
Cu.  ft. 

U-Tube 
Read- 
ing, 
In. 

Baro- 
meter 
In.Mer 

Observed  Temp. 

Calc. 

Disc 

in  Hr. 

in  30  min. 

Water 

cury 

Flow 

"Com- 

Ca 

bined" 

264 

8474 

Mar.   25  \Y2 

22,045 

3.27 

29.4 

59 

63 

1.607 

265 

8251 

26  5 

5,655 

4.51 

29.4 

59 

59 

0.3532 

266 

8151 

27  V/2 

2,048 

4.59 

29.35 

63 

59 

0.1274 

267 

8251 

30  6 

5,780 

4.52 

29.4 

62 

63 

0.3603 

268 

8151 

April     1  QY2 

2,161 

4.64 

29.5 

62 

56^ 

0.1339 

269 

8251 

2  5 

5,590 

4.50 

29.5 

61 

59 

0.3479 

270 

8171 

6  5 

2,742 

4.62 

29.3 

59 

55^ 

0.1696 

271 

8171 

7  ey2 

2,564 

4.61 

29.55 

54 

36K 

0.1644 

272 

8171 

8  8 

2,553 

4.62 

29.65 

54 

29 

0.1658 

273 

8171 

9  6 

2,513 

4.61 

29.5 

55 

34^ 

0.1622 

274 

8151 

18  6y2 

2,000 

4.61 

29.4 

59 

52 

0.1253 

275 

8151 

19  6 

1,866 

4.60 

29.45 

59 

44 

0.1188 

276 

8151 

20  QY2 

1,998 

4.59 

29.4 

64 

60 

0.1238 

This  corrected  value  of  the  quantity  of  air  discharged, 
reduced  to  standard  conditions  of  temperature  and  pressure, 
corresponds  with  the  value  Q  in  formula  [4] .  In  this  formula, 
as  all  the  quantities  but  Cv  are  known,  the  latter  can  be 
calculated.  The  relation  between  Cv  and  Ca,  as  shown  by 
equation  [9],  gives  a  means  of  obtaining  this  latter  value. 
As  stated  earlier  in  the  paper,  the  15  min.  air  constant  was 
the  value  calculated  in  all  the  Joplin  tests.  Ca  is  expressed 
in  thousands  of  feet  for  15  min. 

Summary  of  Results  of  Tests 

About  one  hundred  and  sixty  tests  on  8  and  10  in.  orifice 
meter  discs  were  run  at  Joplin  during  1913-1914.  A  summary 
of  the  results  of  these  tests  is  included  in  Tables  13  to  17  inclu- 
sive. A  note  on  the  system  used  in  numbering  the  discs  will 
make  the  summary  self-explanatory.  The  first  one  or  two 

94 


ORIFICE      METER      MEASUREMENT 


Table  16 — Summary  of  Holder  Tests  on  10  in.  Orifice  Meters 


Test 
No. 

No.  of 
Meter 
Disc 

Date  of 
Test  and 
Duration 
in  Hr. 

Avg.Corr. 
Rate 
Cu.  ft. 
in  30  min. 

U-Tube 
Read- 
ing, 
In. 
Water 

Baro- 
meter 
In.Mer 
cury 

Observed  Temp. 

Calc. 
Ca 

Flow 

"Com- 
bined" 

401 

10401 

Dec.    20  3 

13,978 

4.345 

29.4 

48 

32 

0.9286 

402 

10501 

20  2 

23,156 

3.94 

29.5 

47 

32^ 

1.611 

403 

10501 

20  2 

23,138 

3.94 

29.4 

l&A 

31 

1.620 

404 

10801 

26  1 

53,855 

1.38 

29.4 

45 

2&A 

6.384 

405 

10751 

21  1 

49,513 

1.89 

29.5 

48 

333^ 

4.983 

406 

10801 

21  1 

53,975 

1.38 

29.3 

50 

35 

6.370 

407 

10801 

22     y2 

55,595 

1.43 

29.2 

48 

36 

6.429 

408 

10751 

22  1 

50,575 

1.95 

29.2 

49 

35 

5.025 

409 

10501 

23  2 

23,209 

3.95 

29.2 

49 

32^ 

1.626 

410 

10401 

23  33^ 

14,189 

4.38 

29.2 

48 

33 

0.9406 

411 

10551 

22  iy2 

29,042 

3.89 

29.2 

48 

35^ 

2.035 

412 

10551 

26  iy2 

28,225 

3.68 

29.4 

45 

26K 

2.055 

413 

10751 

27  1 

48,850 

1.90 

29.4 

48 

363^ 

4.976 

414 

10801 

27     % 

55,220 

1.39 

29.4 

49 

37 

6.450 

415 

10501 

27  2 

21,080 

3.28 

29.4 

49 

35^ 

1/605 

416 

10701 

28  1 

45,038 

2.41 

29.5 

46^ 

35^ 

3.986 

417 

10401 

Jan.      5  3 

13,990 

4.31 

29.4 

4sy2 

28^ 

0.9355 

418 

10801 

5  1 

53,363 

1.37 

29.5 

47 

2sy2 

6.368 

419 

10501 

6  2 

23,076 

3.89 

29.3 

49^ 

39 

1.604 

420 

10651 

6  iy2 

39,034 

2.87 

29.3 

50 

40 

3.159 

421 

10551 

7  iy2 

28,593 

3.65 

29.1 

53^ 

493^ 

2.025 

422 

10601 

7  VA 

34,335 

3.27 

29.0 

54 

483^ 

2.581 

423 

10751 

7  1 

50,320 

1.89 

29.0 

55j^ 

473^ 

4.997 

424 

10551 

s  iy2 

28,457 

3.63 

29.0 

52^ 

46 

2.035 

425 

10601 

s  iy2 

34,028 

3.24 

29.0 

49 

W1A 

2.613 

426 

10601 

s  iy2 

34,105 

3.25 

29.0 

51^ 

43 

2.592 

431 

10771 

17  1 

50,952 

1.61 

29.3 

5iy2 

44 

5.474 

432 

10351 

1733^ 

10,890 

4.39 

29.3 

53 

44^ 

0.7067 

433 

10601 

is  iy2 

34,250 

3.31 

29.0 

52 

44 

2.578 

434 

10601 

20  iy2 

33,983 

3.27 

29.2 

52 

42^ 

2.571 

435 

10451 

20  2y2 

18,172 

4.16 

29.2 

50 

38^ 

1.224 

436 

10651 

20  1 

38,922 

2.91 

29.2 

49 

33 

3.174 

437 

10351 

22  sy2 

11,028 

4.44 

29.0 

57 

57 

0.7003 

95 


ORIFICE      METER      MEASUREMENT 


Table  17 — Summary  of  Holder  Tests  on  10  in.  Orifice  Meters 


Test 
No. 

No.  of 
Meter 
Disc 

Date  of 
Test  and 
Duration 
in  Hr. 

Avg.Corr. 
Rate 
Cu.  ft. 
in  30  min. 

U-Tube 
Read- 
ing, 
In. 
Water 

Baro- 
meter 
In.Mer 
cury 

Observed  Temp. 

Calc. 
Ca 

Flow 

"Com- 
bined" 

438 
439 
440 

10651 
10551 
10551 

Jan.    22  \y± 

22  \y2 
23  \y2 

40,104 
14,412 
14,713 

2.92 
3.68 
3.69 

29.0 
29.0 
29.0 

57 
55 

57 

56M 

3.147 
2.015 
2.063 

441 
442 
443 

10751 
10701 
10701 

23  1 
23  1 
24  1 

25,288 
45,510 
44,938 

1.91 
2.39 
2.35 

29.0 
29.0 
29.2 

53 

52 

47^ 

46 

40^ 
34 

5.001 
4.061 
4.076 

444 
449 
452 

10801 
10351 
10451 

24  1 

28  31A 

31  zy2 

53,895 
11,101 
18,329 

1.36 
4.44 
4.23 

29.2 
29.0 
29.4 

46^ 
60 

62 
36 

6.432 
0.7003 
1.226 

454 
456 
457 

10501 
10801 
10351 

Feb.      1  2 
2  1 
2  3 

23,345 
53,800 
10,805 

3.93 
1.37 
4.37 

29.3 
29.3 
29.3 

50 
50 

51 

43 
38 
40 

1.603 
6.337 
0.7085 

458 
459 
460 

10801 
10701 
10351 

3  1 
3  1 

4  4 

53,863 
44,560 
10,751 

1.38 
2.40 
4.46 

29.4 
29.4 
29.2 

48 

47 
47 

33 
30 

6.361 
4.009 
0.7074 

461 
462 
463 

10771 
10771 
10551 

4  1 
6  1 

51,580 
51,187 
27,538 

1.64 
1.65 
3.76 

29.2 
29.4 
29.4 

44 
39 
39 

31M 

5.590 
5.695 
2.054 

465 
466 
467 

10621 
10621 
10621 

11  \y± 
11  iM 

36,934 
36,742 
36,818 

3.12 
3.11 
3.10 

29.3 
29.3 
29.3 

53 

48M 
46 

2.825 
2.818 
2.836 

477 
478 
479 

10301 
10301 
10252 

April  21  6 
22  6 
23  7 

4,059 
4,056 
2,735 

4.49 
4.47 
4.52 

29.4 
29.5 
29.4 

64 
65 
64 

67 
67 

0.5019 
0.5102 
0.3380 

480 

481 
482 

10301 
10252 
10252 

25  61A 
26  7 

27  7 

3,863 
2,707 

2,745 

4.37 
4.53 
4.57 

29.65 
29.3 
29.25 

60 
67 
63 

47 
67 
62 

0.5043 
0.3354 
0.3409 

483 
484 
485 

10301 
10301 
10301 

28  6 
29  6 
30  6 

4,005 
3,990 
3,931 

4.42 
4.48 
4.49 

29.4 
29.6 
29.6 

62^ 
62 
61 

56 
53 
53 

0.5101 
0.5089 
0.4986 

486 

10252 

May      1  6 

2,701 

4.53 

29.4 

62 

553^ 

0.3412 

96 


ORIFICE      METER      MEASUREMENT 

digits  indicate  the  size  of  the  pipe  line  in  which  the  disc  is 
inserted;  the  next  two  digits,  the  size  of  the  orifice;  the  re- 
maining digits,  the  serial  number  of  the  disc.  For  example, 
8473  represents  an  8  in.  meter  disc,  4J4  in.  orifice;  104211  is 
a  10  in.  meter  disc,  4^  in.  orifice,  etc.  It  was  found  necessary 
to  discard  perhaps  half  a  dozen  tests,  on  account  of  their 
disagreeing  widely  from  the  averages  of  the  remainder.  In 
two  or  three  of  these  discarded  tests,  a  shower  or  a  fall  of 
snow  during  the  Itest  furnishes  a  possible  explanation;  in 
other  tests,  no  expanation  was  found. 

It  is  worthy  of  special  note  that  in  these  tests  the  stand- 
ard used  is  an  actual  measurable  volume,  and  not  a  standard- 
ized pitot  tube  or  other  indirect  method  of  measurement. 
The  advantage  of  being  able  to  calibrate  directly  against 
displacement  is  a  most  important  feature  of  these  holder 
tests.  A  second  feature  of  the  tests  is  the  ability  to  auto- 
matically secure  a  practically  constant  flow,  without  regu- 
lation of  any  kind. 

Another  point  deserving  mention  is  the  fact  that  dupli- 
cate discs  of  sizes  already  tested  at  Joplin  require  no  calibra- 
tion of  any  kind.  It  is  merely  necessary  to  micrometer  the 
orifice  and  to  correct  mathematically  for  any  small  deviation 
from  the  nominal  diameter.  For  example,  if  a  new  8  in.  by 
4  in.  orifice  disc  micrometers  4.004  in.  in  diameter,  and  the 
result  of  the  Joplin  tests  on  the  master  8  in.  by  4  in.  orifice 
be  1.034,  the  value  of  Ca  for  the  slightly  oversized  disc  would 
be  1.034  (4.004-^4.000)2  or  1.036. 

The  possibility  of  securing  constants  for  duplicate  discs 
without  actual  calibration  is  a  great  advantage,  as  will  be 
realized.  It  means  that  sufficient  time  and  effort  can  be 
spent  in  calibrating  the  master  discs  to  secure  the  highest 
possible  accuracy,  without  having  the  cost  of  an  individual 
disc  excessively  high.  That  the  method  of  calculating  con- 
stants for  new  discs  as  described  above  is  correct  has  been 
very  well  shown  by  careful  checks  made  at  Joplin. 

97 


ORIFICE      METER      MEASUREMRNT 


Comparison  of  Results  with  Charlottenburg  Tests 


Indicates 
Coefficient 
Values  forl 
Or/f/ce  D/3) 

1 

0" 

b- 

A 

t 

i 

(^ 

f 

// 

/< 

'  Ir 

tc/tcaf&s  Coeffi 
lues  found  a  f 
larlotfenburg  f 
•if  ice  Oisks 

C'er 
or3 

f 

+7_ 

/ 

/- 

V-?- 

-o 

x^ 

&'' 

Oi 

^, 

/?. 

f 

Cot 
Va 
8"C 
'ffH 

•ffic 
'ues 

rifi 
ks 

/en 
for 
ce 

N 

^. 

&& 

•^. 

X'V 

3 

^^~ 

0  10          20         30        40          50         60         70         80         90          100 

Ratio  of    Pipe    Diameter  to  Orifice  Disk  Diameter,  PerCent. 

Fig.    47— COMPARISON    OF     VELOCITY    COEFFICIENTS     OF    ORIFICE 

METER  DISCS,  AS  FOUND  IN  JOPLIN  TESTS  FOR  S  IN.  AND  10  IN. 

PIPE  LINES,  WITH  VALUES  FOUND  AT  CHARLOTTENBURG 

Table  18-  -Summary  of  Values  Plotted 


Joplin  8  in. 

Joplin  10  in. 

Charlottenburg  3%  in- 

d/D 

Cv 

d/D 

Cf 

d/D 

Cv 

0.1875 

64.9 

0.15 

60.1 

0.25 

63.5 

0.219 

64.2 

0.175 

61.1 

0.30 

64.0 

0.25 

64.7 

0.25 

62.8 

0.40 

65.5 

0.3125 

66.9 

0.30 

65.6 

0.50 

73.0 

0.375 

67.9 

0.35 

66.9 

0.60 

81.0 

0.4375 

71.1 

0.40 

67.9 

0.70 

96.0 

0.50 

75.3 

0.45 

70.4 

0.75 

106.0 

0.5625 

79.0 

0.50 

74.9 

0.594 

82.2 

0.55 

78.7 

0.625 

86.6 

0.60 

83.2 

0.655 

91.3 

0.625 

84.6 

0.6875 

95.3 

0.65 

86.6 

0.7187 

100.7 

0.70 

95.9 

0.75 

107.0 

0.75 

103.5 

.... 



0.80 

116.6 



ORIFICE      METER      MEASUREMENT 

The  only  published  report*  of  tests  made  on  orifice  discs 
similar  to  those  tested  at  Joplin  gives  the  values  of  the 
velocity  coefficient,  Cv  (as  used  in  the  fundamental  formula) 
for  3M  m-  pipe  found  in  tests  made  at  Charlottenburg, 
Germany.  Fig.  47  shows  graphically  the  values  found  at 
Charlottenburg  compared  with  the  Joplin  results  for  8  and 
10  in.  p  ipe.  The  Joplin  curves  agree  fairly  well  with  the 
Charlottenburg  values,  especially  if  the  difference  in  the 
pipe  size  is  taken  into  account." 


ERIE  HOLDER  TESTS 

A  subsequent  series  of  calibrations  was  run  in  1915  to 
supplement  the  large  capacity  meters  previously  developed 
by  the  addition  of  a  series  of  relatively  small  capacity  meters 
in  6  in.  and  4  in.  pipe.  The  reference  quantity  chosen  for 
this  work  was  a  small  holder  located  at  the  testing  plant  of 
the  Metric  Metal  Works,  Brie,  Pa.  Check  tests  were  also 
taken  with  8  in.  and  10  in.  pipe  line  orifices;  in  all  about  130 
determinations  were  made  covering  the  following  orifices. 

Table  19 


No. 

Size  of 
Pipe,  In. 

Size  of 
Orifices 
In. 

No. 

Size  of 
Pipe,  In. 

Size  of 
Orifices, 
In. 

4051 

4 

0.506 

6204 

6 

2.002 

4071 

4 

0.755 

6302 

6 

3.003 

4103 

4 

0.996 

6401 

6 

4.000 

4123 

4 

1.250 

8101 

8 

1.010 

4154 

4 

1.500 

8205 

8 

2.006 

4174 

4 

1.754 

8304 

8 

3.006 

4205 

4 

1.997 

8451 

8 

4.500 

4223 

4 

2.251 

8506 

8 

5.005 

4251 

4 

2.504 

10151 

10 

1.500 

4301 

4 

3.002 

10302 

10 

3.007 

6101 

6 

1.002 

10451 

10 

4.502 

6151 

6 

1.502 

10601 

10 

5.999 

*  Zeit.  des  Ver.  d.  Ing.,  Feb.  23,  1908. 

99 


ORIFICE      METER      MEASUREMENT 


100 


ORIFICE      METER      MEASUREMENT 

Table  on  Page  102  gives  data  for  determination  of  leak- 
age in  the  holder  and  lines.  This  gives  a  leakage  correction 
factor  for  these  tests  and  the  dimensions  of  the  holder. 
Table  on  Page  103  is  a  recapitulation  of  the  derivation  of  the 
formula  used  in  determining  the  air  constant  in  this  series 
of  tests.  The  following  is  a  key  to  the  tabulation  employed 
on  the  following  pages. 

Column  Data 

1  Date  of  Test 

2  Size  of  Disc 

3  Barometer  in  inches  of  mercury. 

4  Feet  Drop  of  Holder,  each  foot  drop  is  equiva- 

lent to  displacement  of  200  cu.  ft. 

5  Time  in  Seconds  taken  by  stop-watch. 

6  Ph  Holder  pressure  (Ib.  per  sq.  in.,    absolute). 

7  Th  Temperature  of  holder  air,  deg.  fahr. 

8  T  Temperature  of  flowing  air,  deg.  fahr. 

9  h   Differential  across  disc  inches  of  water. 

10  P  Absolute  pressure,  in  Ib.  per  sq.  in.  on  inlet 

side  of  disc. 

11  Ca  Fifteen-minute  air  constant  for  disc. 

12  Cv  Velocity  coefficient  per  cent. 

Tables  20  and  21  are  specimen  sheets  showing  a  summary 
of  determinations  made  on  various  orifices  in  6  in.  pipe. 

Leakage  Test,  August  7,  1915 — The  readings  and  cal- 
culated results  given  here  show  Leakage  Test  made  to  ascer- 
tain rate  of  leakage  from  holder,  so  proper  allowance  could 
be  made.  This  test  was  started  about  noon  on  a  Saturday 
and  ran  until  early  Monday  morning. 

Time 

Start      11:30  a.  m.  Aug.  7,  1915. 
Finish      7:00  a.  m.  Aug.  9,  1915. 

101 


ORIFICE      METER      MEASUREMENT 


Temperature    of 

Reading 

Readings 

Holder 

of 

deg.    fahr. 

Tape 

Start 

70 

26.0 

Finish 

71 

25.85 

Leakage  (without  any  allowance  for  change  of  temperature 
during  test) :  0. 15  ft.  drop  in  43J/2  nr-  This  is  equivalent  to 
0.0115  cu.  ft.  per  min.  Leakage  (with  temperature  cor- 
rection made): 

0.0130  cu.  ft.  per  min. 

Calculated    Volume    of    Holder,    August    10,    1915 
Measured  Diameter  of  Holder  Top  (Outside). 
16'  0.5";  16'0.1";  15'11.8";  15'11.9";  15/11.7"; 
16'0.1";  15'11.7";  and  16'0.0" 

Average  15'11.975" 

Allowance  for  thickness  of  metal 

2  thickness  No.  16  gauge  iron         0.125" 


Inside  Diameter 


or 


151 1.850" 

15.988  ft. 


Calculated  area  =  200.  76  sq.  ft.  which  means  that  one 
foot  drop  of  holder  displaces  200.76  cu.  ft.  The  nominal 
capacity  is  200  cu.  ft.  per  ft.  drop;  the  actual  capacity  is 
therefore  /^  of  1  per  cent  above  the  theoretical. 

This  error  of  %  of  1  per  cent  in  holder  capacity  is  ignored 
in  the  calculation  of  all  tests  given  in  this  report.  It  exactly 
counter-balances  an  error  of  ^8  of  1  per  cent  in  stop  watch. 

Measured  Circumference  of  Holder 
Near  Top  ............................  50'3%" 

Near  Middle  .........................  50'4" 

Near  Bottom  ........................  .50'4^/ 


102 


ORIFICE      METER      MEASUREMENT 

Derivation  of  General  Formula  for  Calculating  Holder 
Tests  on  Orifice  Meter   Discs. 

Q  =  quantity  measured  under  standard  conditions  of 
pressure  and  temperature,  i.  e.,  60  deg.  fahr.  (520  deg. 
absolute)  and  14.41  Ib.  per  sq.  in. 

Subscript  h  means  actual  conditions  of  air  or  gas  in  holder. 
This  will  vary  from  day  to  day,  even  for  the  same  holder. 

Assuming  Flow  Temp,  of  60  deg.  fahr. 


=  CflV  h  P  for  air, 


=  £<»*/ 
\ 

At  any  other  Flow  Temp.  T 


or       =    <»*  —  —  -  for  gas. 
G 


h  PX520 
T  G 

Furthermore 

520         PL 


ftx520 


In  this  general  formula  derived  above,  there  are  sub- 
stituted special  values  for  reducing  quantity  and  time  of 
test  giving. 

C  =284  6Tape  Difference  (in  ft)  Ph     l~f 


Number  of  Sec.         Th  \  h  P 
103 


ORIFICE      METER      MEASUREMENT 


10 

TH 

Oi 


O 

.g 

CO 

§ 

CO 

•s 

(1) 
H 


00  O  0 
CM  00  CM 

i>  J>  t> 


co  co  co  co  co  CD  CD  CD 


t>  CVJ  CO         COCOLOOjLOCviCO^CO  Oi  CO  LO  LO 

£>-  Oi  t—     LO  i"H  rH  LO  LO  rH  LO  Oi  Oi     CO  rH  CO  Oi     CO  ^  ^  ^ 

rH  rH   ,-H   rH  O  O  O  O 


CM  >— I  Oi  CM         Oi  00  CM  -— I 

inm-^m      mminm 


in 

Tf  CO  CO 

co  io  oo 

Ttf    Tj<    CO 


o      m 

t-t~00t>!—  I 

r-HCOCO'-Ht—  I 


CMOOCOCO         CiCOOir^ 
r-(05CM'-l  CM-^rHCO 

COCMCMCO         m^'cOCAJ 


O5O5O5O5Oii—  Ir-Hr-li-H 


CO  CO  CO         CO  CO  CO  00 

in  in  m 


.— l  .— l  .— (         i— li— l.— lr-H.-HCMCMCMCM         CMCM 

CO  CO  CO    CO  CO  CO  00  CO  CO  00  CO  00    00  CO 

in  in  in   in  in  in  in  in  in  in  in  in   in  in 


® 


00  00  CO    00  CO  00  00  CO  00  00  00  00    00  CO  00  00    00  00  00  00 
CO  CO  CO    CO  CO  CO  CO  CO  CO  CO  CO  CO    CO  CO  CO  CO    CO  CO  CO  CO 


o  t-  m 

i—  1  OJ  00 
CO  CO  lO 
<M  <M  C\J 


rHt-coco  ooco^m 

cooiT^m  oiddd 

cococico  co^t"-^-^ 

i-Hr-fr- 1,— I  CMCMCMCM 


rH  ,-H  •-(  00  00   00  00 


o  oo  m  o 
in  ^  oo  t>- 

^  00  »^  O 


oooo      minmin 

CO  CO  CO  CO         CO  CO  CD  CO 


lO 
1—  1 

t-  i-H  CVJ  CO 


r- 1  CM         CO-^mCD         £>OOO5O 


00 


104 


ORIFICE      METER      MEASUREMENT 


CO  CO  CO  CO  CO 


r-ICOO         Ol  t-  CO  CO 


CO  CO  CO  CO  CO  CO  CD 


Tt<  CO 
CO  CM 
CO  CO 


lOOOCOCOlOi—  llO 
CM  CM  rH  CO  >-H  CO  Tfr*         ^  rH  CO  lO 
CO  CO         O  O  G^  00 
CO  CM  CM 


CM  CO  CO  CO  CO  CO  CO  CO  CO 


OOOOO  OOOOOOO  OOOOOOOOO  rH  rH  rH  rH 


OOOb-tO^C^rH         ^Ht-COOiOCOiOCOiO         CO  CO  >—  I  O5 
CDiOkOkOkOiOiO         £>COCDiOiOiCiOiOiO         CDCDCDkO 


Q5  tO  tO  ^  rH         Oi  Oi  O  rH  00  CO  CO         CO  tO  Qi 
CVJ   CO  tO  tO  00  rH  CO  CO  tr—  CVJ   t*  rH  rH   O  Oi 

10  rt<  CO  CM  r-i         lO^^OQCOCMCM         LO^CM 


CO  00  CO  CO  CO    CO  CO  CO  CO  CO  CO  CO  CO  CO    CO  CO  CO  CO 
tO  tO  tO  tO  tO    tO  tO  tO  tO  tO  tO  tO  tO  tO    tO  tO  tO  tO 


cocococgcococg 


Tj<   T^   Tt<   Tj<   Tj< 


Tf  rf  GO  lO  i—  i  rH  lO         COCOiOC<IiOOiiOOii>-         r—  I 


i—  i  rH  lO 
rHC^JCO 


00  CO 
iOkO 


OOOOO        t- O  O  O  O  O  CM 


05t>0000 

t>  t>  CO  CO 


COCOCOCDCOCOCOCOCO         COCOCOCD 
OiOSOiOSOi         O5OiOiO5OiO5Oi         C5OiO5O5OlOiCiO5O5         OiOiOiOS 


OOOOO 

rH  rH  rH  rH  rH 
CO  CO  CO  CO  CO 


(MCvi(M<>JO3 

CO  CO  CO  CO  CO 


TfTf'^ 
CO  CO  CO 


105 


ORIFICE      METER      MEASUREMENT 

It  will  be  noted  that  there  are  a  few  minor  changes  in 
the  coefficients  in  the  Tables  in  Part  4. 

These  changes  are  very  slight  and  are  caused  by  some 
errors  in  the  original  work. 

Status  of  Coefficient 

Fig.  50  shows  the  degree  of  variation  under  the  con- 
ditions of  the  different  tests,  and  the  solid  black  line  is  an 
averaging  line  on  which  coefficients  for  actual  use  at  the 
present  time  are  based. 

All  the  orifice  calibration  work,  up  to  and  including  the 
Brie  tests,  has  been  compiled  and  reduced  to  a  basis  shown 
in  Pages  108  and  109,  showing  the  "coefficient  of  velocity"  for 
all  sizes  of  pipe  plotted  on  a  basis  of  the  ratio  of  diameters 
of  orifice  to  diameters  of  pipe. 


Fig.  49— ORIFICE  FLANGE  METER  AND  LIGHT  PORTABLE  DIFFERENTIAL 
GAUGE,  PIPE  TAP  CONNECTIONS 


106 


ORIFICE      METER      MEASUREMENT 


TESTS 
Mcer*| 
TESTS 


Size 


OF  ORIFI 


/NCHCS 


50 


107 


ORIFICE      METER      MEASUREMENT 


108 


ORIFICE      METER      MEASUREMENT 


.55 


fi 


h^4+ 


frrrr 


&SO 


m 


K 


m 


ffttt+fflfewifrp 


m 


-± 


mm 


/.oso 


1.000 


.850 


.800 


.750 


.70 


.75" 


109 


ORIFICE      METER      MEASUREMENT 

It  is  the  belief  of  the  author  that  this  value  may  be 
safely  applied  within  the  limits  of  accuracy  shown  by  the 
curve  to  any  practicable  size  of  pipe  line  without  further 
question.  The  number  of  experiments  which  are  incor- 
porated in  it,  and  the  great  variety  of  conditions  under  which 
it  has  been  developed,  have  practically  eliminated  any  per- 
sonal equation  of  observational  error  of  any  individual  test 
or  series  of  tests. 

MEASURING  FLOW  OF  FLUIDS 

The  relation  between  the  differential  and  the  velocity  of 
the  fluid  through  the  orifice  is  expressed  by  the  formula : 


where  V  =  velocity  of  flowing  fluid  in  feet  per  second. 

g  =  acceleration  due  to  gravity  in  feet  per  sec. 
H  =  differential  expressed  in  feet  head  of  flowing  fluid. 

As  it  is  not  practical  to  register  this  value  directly,  the 
differential  is  recorded  on  the  chart  in  inches  of  water  pres- 
sure. 

Cv  =  Coefficient  of  Velocity.  It  is  the  ratio  of  the  actual 
velocity  to  the  theoretical  velocity  of  fluid  passing  the 
orifice.  Its  value  depends  upon  the  ratio  of  the  diameter  of 
the  orifice  to  the  diameter  of  the  pipe,  and  the  location  of 
pressure  connections  with  respect  to  the  orifice. 

The  Coefficient  of  Velocity  is  the  same  for  the  same  ratio 
of  diameter  of  orifice  to  diameter  of  pipe,  i.  e.,  the  value  of 
Cv  for  a  two  inch  orifice  in  a  four  inch  pipe*  is  the  same  as  for 
a  three  inch  orifice  in  a  six  inch  pipe  or  a  four  inch  orifice  in 
an  eight  inch  pipe.  These  coefficients  do  not  bear  a  simple 
mathematical  relation  to  the  ratios  of  diameters  but  they  in- 
crease as  the  ratio  of  diameter  of  orifice  to  diameter  of  pipe 

*  Actual  Dimension. 

110 


ORIFICE      METER      MEASU  RE  M  E  N  T 

increases.  A  two  inch  orifice  in  a  three  inch  pipe  has  a 
greater  coefficient  than  a  two  inch  orifice  in  a  four  inch  pipe. 
The  reason  for  this  is  that  the  nearer  the  size  of  the  orifice 
approaches  the  size  of  the  pipe  line  the  more  closely  the  flow 
approaches  a  jet  effect  and  vice  versa.  With  a  small  orifice 
in  a  large  pipe  the  effect  produced  is  nearer  that  resulting 
from  passing  the  fluid  through  a  small  opening  in  a  drum  or 
storage  tank. 

When  the  pressure  connections  are  located  at  the  flange 
the  values  of  the  "coefficient  of  velocity"  are  lower  than 
when  placed  farther  from  the  flange. 

The  values  of  Cv  for  various  ratios,  diameters  of  orifices 
and  pipes  are  given  on  Pages  108  and  109.  They  apply 
for  any  fluid,  whose  viscosity  is  equal  to  or  less  than  the 
viscosity  of  water. 

As  the  Hourly  Orifice  Coefficient  varies  with  the  "co- 
efficient of  velocity"  it  is  changed  by  any  change  affecting 
this  factor. 

The  following  examples  illustrate  the  application  of  the 
modified  formula  V  =  Cv  V  2  gH  to  the  flow  of  various  gases 
and  liquids  through  a  pipe  line.  It  is  not  practical  to  use 
this  method  of  computation  for  routine  work  but  the  solu- 
tion of  the  examples  demonstrate  the  fundamental  princi- 
ples of  orifice  meter  flow. 

EXAMPLE — Air  being  measured;  atmospheric  pressure, 
14.4  lb.;  line  or  static  pressure,  28.8  lb.;  temperature,  GOdeg. 
fahr.;  diameter  of  orifice,  2  inches;  diameter  of  pipe,  4.026 
inches;  differential,  17  inches  of  water;  pressure  connections 
at  2  J/2  and  8  diameters  from  orifice. 

Absolute  Pressure  P=  14.4+28.8  =  43.2  lb.  per  sq.  in. 
Absolute  Temperature  T  =  60+460  =  520  deg.  fahr. 

Diameter  of  Orifice     2.000 

Ratio  X  = = =  .497 

Diameter  of  Pipe      4.026 

111 


ORIFICE      METER      MEASUREMENT 


C,  for  a  ratio  of  .497  =  736  (Page  108). 

„     1000^  T     1000X17X520 

H  =  —       -  =—  —  =  394  feet  of  air  at  43.2  Ib. 

520PG      520X43.2X1 

absolute  at  60  deg.  fahr.     (Page  64.) 


V  =  CV^  2gH=. 736  V  2X32.16X394  =  117.2  ft.  per  sec. 
Area  of  2  inch  Orifice  =  .0218  sq.  ft.  (Page  75) 

The  quantity  per  second  equals  the  area  of  the  orifice  in 
square  feet  multiplied  by  the  velocity  in  feet  per  second. 

Quantity  =.0218 XI  17.2  =  2.55  cubic  feet  per  second  at 
43.2  Ib.  absolute,  at  60  deg.  fahr. 

2.55X43.2 
Quantity  based  on  14.4  Ib.  per  sq.  m.  =  — 

14.4 

7.65  cubic  feet  per  second. 

Quantity  per  hour  =  7.65X60X60  =  27,500  cu.  ft.  at  at- 
mospheric pressure. 

EXAMPLE — Gas  being  measured;  period,  24  hours;  pipe 
line,  4  inches  (actual  inside  diameter  4.026  inches) ;  diameter 
of  orifice,  2%  inches;  average  differential  pressure,  54  inches 
of  water;  atmospheric  pressure,  14.5  Ib.;  line  pressure,  105.5 
Ib.;  Pressure  Base,  8  oz.  above  atmospheric  pressure ;  Base 
and  Flowing  Temperature,  60  deg.  fahr.  Specific  Gravity, 
0.60;  pressure  connections  at  2^  and  8  diameters  from 
orifice. 

_,          v     Diameter  of  Orifice     2.625 

Ratio  X  =  —  —= =.652 

Diameter  of  Pipe       4.026 

Cv  for  a  ratio  of  .652  =  .901     Page  109. 
Flowing  Temperature  =  460 + 60  =  520  deg.  fahr.  absolute . 
Static  or  Line  Pressure    =105.5  +  14.5  =  120  Ib.  per  sq. 
in.  absolute. 

Pressure  Base  =  0.5+ 14.5  =  15.0  Ib.  per  sq.  in.   absolute. 

112 


ORIFICE      METER      MEASUREMENT 


„  1000X54X520     __n  ,    .  ,       ,     ,    . 

H  =  —       -  =  —  -  =  750  feet  head  of  air  at  120 

520PG     520  X 120  X. 60 

Ib.  absolute  at  60  deg.  fahr.     Page  64. 


.901  V 2X32.16X750- 197.9  feet  per  sec. 
Area  of  2%  inch  Orifice  =  .03758  sq.  ft.   (Page  75) . 

Quantity  per  second  equals  area  of  orifice  multiplied  by 
the  velocity  =.03758X197.9  =  7.44  cubic  feet  of  gas  per 
second  at  120  Ib.  per  square  inch  absolute. 

7  44 x 120 
Quantity,  at  15  Ib.  per  square  inch  absolute  =  — 

15 

59.5  cu.  ft.  per  second ;  for  24  hours  =  24  hours  X  60  minutes  X 
60  seconds  X  59.5  cu.  ft.  per  second  =  5, 140,000  cu.  ft.  per  day. 

In  these  examples  it  is  noted  that  the  differential  when 
expressed  in  feet  head  of  flowing  gas  or  air  is  decreased  as  the 
pressure  increases  and  that  the  volume  when  expressed  at  a 
Pressure  Base  is  increased  as  the  static  pressure  increases. 

EXAMPLE— Water  being  measured;  diameter  of  orifice, 
2  inches;  diameter  of  pipe,  4  inches  (standard);  differential, 
1.84  inches  of  mercury  (pressure  connections  and  U  gauge 
above  mercury  filled  with  water);  pressure  connections  at 
2J/2  and  8  diameters. 

2  00 

Ratio  diam.  of  orifice  to  diam.  of  pipe,  X  =  — - —  =  .497. 

4.026 

Cv  for  ratio  .497  =  .736.     (Page  108). 

Inasmuch  as  the  gauge  and  gauge  connections  are  filled 
with  water,  each  inch  of  mercury  differential  is  offset  by  an 
inch  of  water  so  that  1  inch  of  mercury  indicates  only  12.6 
inches  of  water  pressure  differential  due  to  flow.  Therefore, 
the  pressure  differential  is  1.84X12.6  =  23.2  inches  of  water. 
See  Page  38. 

113 


ORIFICE      METER      MEASUREMENT 


00    O 

=  —  =  1.93  feet  head  of  water. 
12 


=  .  736V  2X32.16X1.93 
F  =  8.20  feet  per  second. 
Area  of  Orifice  =  .0218     (Page  75). 
Quantity=.0218X8.20  =  .179  cu.  ft.  per  second. 
Therefore,  the  quantity  per  hour   =.179X7.48X3600  = 
4820  gallons  per  hour,  where  one  cu.  ft.  equals  7.48  gallons. 

EXAMPLE — Oil  being  measured;  diameter  of  orifice,  2 
inches;  diameter  of  pipe,  4.026  inches;  differential,  1.84 
inches  of  mercury,  gauge  lines  and  gauge  filled  with  oil; 
Baume  gravity,  30  degrees;  viscosity,  25  seconds  Saybolt. 
(in  this  case  the  viscosity  of  the  oil  is  less  than  that  of  water 
and  therefore  the  coefficient  of  velocity  for  the  oil  is  the  same 
as  coefficient  of  velocity  for  air. 

Diameter  of  Orifice     2.000 

Ratio  X  =  —         = =  .497 

Diameter  of  Pipe      4.026 

Cv  for  .497  ratio  =  .736     (Page  108) 

As  the  specific  gravity  of  this  oil  is  .875  compared  with 
water,  each  inch  of  mercury  =  13. 6/. 875  =  15.54  inches  of  oil, 
but  each  inch  of  mercury  differential  is  offset  by  a  pressure 
equal  to  one  inch  of  oil  and  therefore,  each  inch  of  mercury 
differential  indicates  15.54 — 1.00  or  14.54  inches  of  oil  dif- 
ferential. Therefore,  the  differential  pressure  =  1.84X14. 54 
=  26.8  inches  of  oil  =  2.23  ft.  See  Page  38. 


V  =  CV  V  2gH=  .736  V  2X32.16X2.23  =  8.81  feet  per  sec. 

Quantity  =  .0218  X  8.81  feet  per  second  =  .192  cubic  feet 
per  second  =  691  cubic  feet  per  hour  =  691/5.615  or  123  barrels 
per  hour,  where  5.615  cubic  feet  equals  one  barrel. 

In  the  case  of  oil  and  water  the  amount  measured  is  de- 
pendent only  on  the  differential.  The  pressure  does  not  pro- 
duce any  effect  on  the  volume  or  the  differential. 

114 


ORIFICE      METER      MEASUREMENT 

To  simplify  all  calculations  for  orifice  meter  measurement 
the  values  of  H  (the  differential  in  feet  head  of  flowing  fluid) , 
have  been  expressed  in  terms  of  inches  of  water  differential 
for  liquids  and  in  terms  of  inches  of  water  head  and  pressure 
in  pounds  per  square  inch  absolute  for  air,  gases  and  vapors. 
The  multipliers  used,  the  area  of  the  orifice  and  units  of 
measurement  are  combined  in  one  term,  for  the  conditions 
of  flow  at  any  orifice.  This  term  is  known  as  the  Hourly 
Orifice  Coefficient  C,  which  is  used  in  the  following  simple 
formulae.  It  is  the  volume  per  hour  at  a  one  inch  differential 
(in  cases  of  gases  at  1  Ib.  per  square  inch  absolute). 

For  gases  Q  = 
For  liquids  Q  = 
Where  Q   =   quantity  per  hour  expressed  in  weight 
or  volume. 

C  =  Hourly  Orifice  Coefficient.  '  This  value  does  not 
change  for  any  orifice  when  measuring  fluids 
of  the  same  specific  gravity.  The  coefficient 
for  an  orifice  of  any  commercial  size  for  gas, 
air,  steam,  water,  oil,  etc.,  are  contained  in  the 
tables  in  this  volume. 

h  =  the  differential  pressure  existing  between  the  two 
pressure  connections  expressed  in  inches  of 
water  head,  this  value  being  recorded  graphical- 
ly on  the  chart  of  the  recording  differential 
gauge. 

P  =  the  static  pressure  expressed  in  absolute  units, 
being  equal  to  the  atmospheric  pressure  plus 
the  gauge  pressure  (which  is  recorded  on  the 
chart).  The  value  of  the  gauge  pressure  is 
also  recorded  on  the  chart. 

In  measuring  liquids  the  static  pressure  is  ignored  as 
liquids  are  nearly  incompressible. 

115 


ORIFICE      METER      MEASUREMENT 

Extensions  of  the  value  of  V  hP  for  differential  pres- 
sures from  1  to  100  inches  water  head  and  for  all  static 
pressure  ranges  from  29  inches  mercuiy  vacuum  to  500  Ib. 
gauge  pressure  are  contained  in  the  book,  "Pressure  Exten- 
sions," published  by  this  company. 

For  a  detailed  explanation  of  the  above  formulae  and  their 
application  to  the  measurement  of  air,  gas,  steam  and  liquids, 
the  reader  is  referred  to  the  Parts  4,  5,  6,  and  7. 


Fig.  53— DIFFERENTIAL  GAUGE,  10  INCH  DIFFERENTIAL  RANGE 


116 


ORIFICE      METER      MEASUREMENT 

MERCURY    FLOAT    TYPE    DIFFERENTIAL 
GAUGES 

As  iron  weighs  approximately  .26  Ib.  per  cubic  inch,  and 
mercury  weighs  approximately  .49  Ib.  per  cubic  inch — iron 
will  float  in  mercury.  This  makes  a  very  desirable  com- 
bination for  a  differential  gauge,  as  the  mercury  is  a  very 
sensitive  liquid  and  will  not  freeze  above  a  temperature  of 
40  deg.  fahr.  below  zero. 

The  mercury  float  type  differential  gauge  is  primarily 
a  U  tube  made  of  semi-steel  and  steel  in  which  mercury  is 
used  as  a  seal.  A  cast  iron  or  steel  float  which  floats  in  the 
mercury  is  placed  in  either  the  high  or  low  pressure  column 
of  the  U  tube  and  is  connected  by  a  lever  and  shaft  (working 
through  a  stuffing  box)  with  the  pen  arm.  The  pen  of  the 
pen  arm  records  on  a  chart  which  is  rotated  by  clock  work. 

Some  of  the  gauges  are  constructed  with  the  one  column 
of  the  U  tube  surrounding  the  other  column.  Fig.  35 
illustrates  such  a  gauge  in  which  the  high  pressure  column 
surrounds  the  low  pressure  column  and  in  which  the  float 
rests  in  the  mercury  in  the  low  pressure  column.  Fig.  54 
illustrates  a  type  of  gauge  which  resembles  the  ordinary  U 
tube.  In  this  type  also  the  float  rests  in  the  mercury  in 
the  lower  pressure  column. 

The  line  pressure  upstream  from  the  orifice  is  admitted 
to  column  H  and  the  downstream  pressure  to  column  L,  so 
that  both  columns  are  under  line  pressure.  The  recording 
parts,  clock,  etc.,  which  are  contained  in  the  case,  are  under 
the  atmospheric  pressure. 

In  Fig.  54  when  the  pen  is  in  the  zero  position  the  float 
is  raised  about  one-eighth  inch  above  the  bottom  of  the 
column  L.  As  the  pressure  in  column  H  increases  over  the 
pressure  in  column  L,  the  mercury  lowers  in  column  H  and 
rises  in  column  L,  raising  the  float.  The  rise  and  fall  of  the 
float  is  transmitted  .by  the  lever  and  shaft  to  the  pen  arm 
which  indicates  on  the  chart  the  rise  and  fall  of  the  mercury 

117 


ORIFICE      METER      MEASUREMENT 

in  the  column  in  which  the  float  is  placed.  The  charts  used 
are  graduated  in  inches  of  water  differential  to  indicate 
the  difference  of  pressures  acting  in  the  columns  of  the  gauge. 
For  each  13.6  inches  of  water  differential  the  difference  in 
the  elevation  of  mercury  in  the  two  columns  is  one  inch. 
For  27.2  inches  of  water  the  difference  is  2  inches  of  mercury, 
etc.,  so  that  for  each  inch  increase  of  water  differential 
recorded  on  the  chart  the  increased  difference  in  the  mer- 
cury levels  of  the  two  columns  is  .0735  inch.  Therefore,  for 
a  20  inch  water  differential  the  difference  in  mercury  levels  is 
1.47  inches.  At  the  zero  position  the  surfaces  of  the  mer- 
cury in  the  two  columns  are  on  the  same  level  but  due  to 
the  difference  in  areas  of  the  columns,  the  mercury  in  the 
column  H  will  fall  more  rapidly  than  it  will  rise  in  column  L. 
For  instance,  if  column  L  is  four  times  the  area  of  column 
H,  for  each  inch  of  mercury  differential  the  mercury  will  fall 
.8  of  an  inch  in  column  H  while  it  rises  .2  of  an  inch  in  column 
L.  This  is  necessarily  so  because  the  volume  of  mercury 
displaced  in  the  one  column  must  be  equal  to  the  volume  of 
mercury  added  to  the  other  column.  In  differential  gauges 
where  the  chambers  or  columns  are  uniform  in  area  through- 
out the  column,  each  equal  increase  of  differential  will  cause 
an  equal  increase  in  rise  in  the  column  L  and  consequently, 
an  equal  increase  in  rise  of  the  float.  Providing  the  arc  over 
which  the  float  joint  travels  is  small  the  pen  attached  to  the 
differential  arm  will  travel  over  equal  spaces  on  the  chart  for 
equal  increases  of  mercury  differential. 

The  pressure  which  causes  the  float  to  rise  is  equal  to  the 
area  of  the  float  multiplied  by  the  distance  through  which  the 
mercury  rises  for  each  increase  in  differential  by  the  weight 
of  mercury  per  cubic  inch,  and  the  force  which  tends  to 
overcome  the  friction  of  the  shaft  in  the  stuffing  box  is  equal 
to  this  pressure  multiplied  by  the  length  of  the  float  lever. 
Therefore,  it  is  evident  that  the  larger  the  float  and  the 
longer  the  lever  the  more  force  there  is  to  overcome  the 

118 


ORIFICE      METER      MEASUREMENT 


CHECK  VALVE 


DOWNSTREAM 
CONNECTION 


FLOAT   LEVER 

F 


UPSTREAM 
CONNECTION 


CHECK  VALVE 


PRESSURE 
SPRING 


COLUMN   H 

DIFFERENTIAL 
PRESSURE 
PEN   ARM 


Fig.  54— SECTIONAL  VIEW  OF  A  100  INCH  DIFFERENTIAL  AND 
STATIC  PRESSURE  GAUGE 

THE  50  INCH  GAUGE  IS  SIMILAR  IN  DESIGN 


119 


ORIFICE      METER      MEASUREMENT 

friction  of  the  stuffing  box,  hence  greater  sensitiveness. 
There  must  be  friction  in  stuffing  boxes  as  it  is  the  friction 
only  which  prevents  leakage.  The  friction  in  the  stuffing 
box  may  be  reduced  by  using  a  smaller  pin  through  the 
stuffing  box  but  there  is  a  limit  to  the  size  of  this  pin  due  to 
the  bending  effect  which  may  be  caused  by  the  weight  of  the 
pen  arm. 

Due  to  the  fact  that  the  travel  of  the  pen  is  proportional 
to  the  rise  of  the  float  and  the  length  of  the  float  lever,  if 
when  checking  a  gauge  against  a  water  column,  at  zero  check 
the  pen  is  on  the  zero  line  and  at  20  inches  on  the  water 
column  the  pen  rests  on  the  19  inch  line,  and  when  the  water 
column  indicates  40  inches,  the  pen  is  slow  and  rests  at  38 
inches,  it  is  evident  that  a  reduction  of  the  effective  length 
of  the  float  lever  will  cause  the  pen  arm  to  move  more  rapidly. 
If  the  distance  between  the  float  joint  and  the  shaft  is  de- 
creased by  one  twentieth  (in  this  case)"  the  pen  will  record 
correctly.  The  mercury  will  always  register  the  proper  dif- 
ferential, but  the  levers,  etc.,  may  not  be  in  proper  adjust- 
ment to  indicate  correctly  in  inches  of  water. 

All  mercury  float  type  gauges  which  are  exposed  to  the 
elements,  are  subject  to  temperature  variations  due  to  the 
fact  that  the  mercury  expands  when  the  temperature  in- 
creases, and  contracts  when  the  temperature  decreases. 
This  statement  also  applies  to  steel.  The  cubical  expansion 
of  mercury  for  1  deg.  fahr.,  is  .000099,  and  the  cubical 
expansion  of  steel  is  .000017,  so  that  the  difference  between 
cubical  expansion  of  mercury  and  of  steel  causes  a  rise  of  the 
mercury  for  a  50  degree  increase  in  temperature  which  will 
produce  a  movement  on  the  pen  arm  in  a  50  inch  gauge, 
equivalent  to  %  of  1  inch  of  water  pressure  and  vice  versa. 
If  a  gauge  of  this  type  is  set  on  zero  in  the  cool  part  of  the 
day  and  the  temperature  of  the  mercury  rises  50  degrees 
during  the  day,  when  the  gauge  is  again  checked  for  zero  at 
the  time  when  the  temperature  is  the  greatest  the  pen  arm 

120 


ORIFICE      METER      MEASUREMENT 

will  be  about  Y&  of  an  inch  above  the  zero  line.  From  the 
above  it  may  be  thought  that  this  error  could  be  eliminated 
by  using  less  mercury,  but  in  all  types  of  gauges  which  use 
lesser  quantities  of  mercury,  the  area  of  the  chambers  is  also 
decreased,  or  the  ratio  of  the  rise  of  the  float  to  the  movement 
of  the  pen  arm,  is  decreased,  so  that  the  net  effect  on  all 
gauges  is  approximately  the  same.  The  error  due  to  a  50 
degree  change  of  temperature  will  make  a  difference  equi- 
valent to  one-third  of  one  per  cent  of  the  maximum  range  of 
the  gauge.  Therefore,  to  eliminate  this  discrepancy  the 
gauge  should  be  sheltered  and  protected  from  extreme  tem- 
perature changes. 

ACCURACY  OF  ORIFICE  METER 

The  Orifice  Meter  and  its  Differential  Gauge  are  like  the 
Large  Capacity  Meter.  When  given  proper  attention  they 
will  give  results  as  accurate  as  any  measuring  instrument 
known. 

A  great  many  users  have  the  impression  that  the  orifice 
is  the  main  part  of  the  meter  and  therefore  cannot  "get  out 
of  order."  While  it  is  true  that  the  orifice  itself  will  not 
easily  change  its  diameter  or  shape  or  "get  out  of  order," 
the  Differential  Gauge  is  a  delicate  recording  instrument 
and  must  be  checked  periodically  and  kept  in  good  condi- 
tion, free  from  condensation.  In  addition  to  this  it  is  very 
important  that  the  coefficient  be  based  on  the  true  conditions 
of  the  gas  or  liquid  measured. 

The  weighing  or  measuring  device  that  will  not  become 
inaccurate  at  some  time  or  other  has  not  been  invented. 
Even  the  measuring  rule  will  shrink  as  it  grows  older. 

Another  point  that  is  seldom  considered  by  users  of 
Orifice  Meters,  is  that  when  a  differential  gauge  is  out 
of  adjustment  and  the  pen  arm  reads  too  low  or  too  high, 
the  error  is  not  expressed  in  percentage  figures. 

121 


ORIFICE      METER      MEASUREMENT 


122 


ORIFICE      METER      MEASUREMENT 

For  instance,  if  the  differential  pen  arm  records  two 
inches  in  error,  it  is  spoken  of  as  merely  two  inches  too 
high  or  too.  low,  and  the  error  is  seldom  expressed  in  per 
cent.  The  percentage  of  error  due  to  a  differential  pen  arm 
recording  too  high  or  too  low  is  dependent  on  whether  the 
differential  pressure  is  ranging  around  a  low  or  a  high  value. 
If  the  differential  pressure  should  average  10  inches  of  water 
pressure  and  the  pen  arm  should  be  found  to  be  recording 
two  inches  too  high  or  too  low,  the  error  would  be  12  per  cent 
fast  or  9  per  cent  slow.  While  if  the  differential  pressure 
should  range  between  40  and  44  inches  of  water  pressure 
with  the  same  error  of  2  inches  in  the  differential  pen  arm  the 
error  would  be  about  2.5  per  cent. 

The  error  due  to  an  erratic  static  pressure  pen  arm  or  a 
static  pen  arm  that  records  too  low  or  too  high  can  likewise 
be  expressed  in  percentage  figures.  The  percentage  fast  or 
slow  varies  according  to  the  static  pressure  of  the  gas  mea- 
sured. It  is  greatest  for  low  pressure  and  smallest  for 
high  pressure.  If  the  static  pressure  pen  arm  reads  2  Ib. 
high  at  atmospheric  pressure,  the  percentage  fast  would  be 
6.7.  If  the  static  pressure  ranges  around  400  Ib.  and  the 
static  pen  arm  records  2  Ib.  high,  the  error  would  be  0.24 
per  cent  fast. 

From  the  foregoing  the  reader  will  note  there  is  greater 
necessity  of  having  both  the  static  and  differential  pen  arms 
recording  more  accurately  at  low  pressures  than  at  high 
pressures. 

In  addition  to  any  error  from  an  erratic  static  or  dif- 
ferential pen  arm,  the  error  constantly  exists  if  the  coeffi- 
cient is  not  revised  for  the  true  conditions,  for  instance, 
specific  gravity  when  measuring  gas.  If  the  orifice  coefficient 
is  based  on  a  specific  gravity  of  .6  and  the  true  specific 
gravity  of  the  gas  measured  is  .65,  the  result  would  be  4  per 
cent  too  high,  or  if  the  coefficient  was  based  on  a  specific 

123 


ORIFICE      METER      MEASUREMENT 

gravity  of  .65,  and  the  true  specific  gravity  of  the  gas  was  .6, 

the  result  would  be  4  per  cent  too  low. 

To  give  an  example  where  all  three  errors  occur : 
Assume  that  the  differential  pen  arm  was  marking  two 

inches  high  and  the  static  pressure  pen  arm  was  marking 

two  pounds  high,  also  that  the  true  gravity  of  the  gas  was 

.70  instead  of  .65  upon  which  the  coefficient  was  calculated. 
Using  an  hourly  coefficient  of  1000,  differential  12  inches 

of  water,  and  static  pressure  12  lb.,  then  the  formula  would 

read: 

100 V 12  (14.4+ 12)  =  17,799  cu.  ft. 

With  the  differential  pen  arm  marking  two  inches 

too  high,  deduct 8  per  cent 

With  the  static  pen  arm  marking  two  lb.  too  high, 

deduct 4  per  cent 

To  correct  for  true  gravity  of  gas  from  .65  to  .70, 

deduct 4  per  cent 


Total  per  cent  fast  16  per  cent. 

17,799X84%  =  15,051  cu.  ft. 

To  prove  error,  change  formula  to  read  with  correct 
pressures : 

100 V   10  (14.4+ 10)  =  15,621  cu.  ft. 

To  correct  this  result  for  change  in  specific  gravity  from 
.65  to  .70: 

15,621  X  .9636  - 15,052  cu.  ft. 

In  giving  the  foregoing  or  following  facts  and  figures  it  is 
not  the  intention  of  the  author  to  discredit  the  accuracy  of 
the  Orifice  Meter  as  a  measuring  instrument,  but  to  put 
forth  the  true  facts  in  such  a  light  that  the  orifice  meter  users 
will  fully  understand  what  the  different  errors  mean  in  per- 
centage figures,  and  to  create  a  better  understanding  of  this 
type  of  meter,  that  greater  accuracy  may  be  obtained. 

124 


ORIFICE      METER      MEASUREMENT 


125 


ORIFICE      METER      MEASUREMENT 


Table    22 
DIFFERENTIAL  GAUGE  CAPACITIES 

Capacity  ranges  of  Differential  Gauges.     Same  Orifice  and  Pipe. 
Hourly  Orifice  Coefficient  100. 


Maximum 

Closest 

Minimum 

Ratio  of 

Reading 

Maximum 

Reasonable 

Chart 

Minimum 

Maximum 

Chart 

Capacity 

Reading 

Reading* 

Capacity 

to  Mini- 

Inches 

Inches 

Inches 

mum   Flow 

100 

1000 

0.4 

8.0 

283 

3.5 

50 

707 

0.2 

4.0 

200 

3.5 

25 

500 

0.1 

2.0 

141 

3.5 

20 

447 

0.08 

1.6 

127 

3.5 

10 

316 

0.04 

0.8 

89 

3.5 

2.5 

158 

0.01 

0.2 

45 

3.5 

*Minimum  chart  reading  corresponds  to  a  2J^  per  cent  devia- 
tion in  results  for  the  closest  reasonable  reading. 

The  above  Table  is  self  explanatory  and  is  given  to 
illustrate  the  capacity  relations  of  various  ranges  of  gauges, 
also  the  fact  that  the  ratio  of  maximum  to  minimum  flow 
is  the  same  regardless  of  the  maximum  differential  range  of 
the  chart,  when  we  use  the  same  standard  for  determining 
the  minimum  chart  reading  which  ultimately  is  the  limit  of 
ordinary  vision.  The  maximum  capacity  for  a  100  inch 
gauge  is  twice  as  great  as  for  a  25  inch  gauge,  but  it  is  likewise 
true  that  the  minimum  capacity  of  the  100  inch  gauge  is 
also  twice  as  great.  The  relative  capacities  are  based  on  an 
Hourly  Orifice  Coefficient  of  100  for  water.  The  relations 
shown  are  the  same  for  any  liquid,  or  a  gas  at  a  definite 
pressure. 

DIFFERENTIAL  RANGE 

There  are  many  who  advocate  the  50  inch  differential 
pressure  range,  and  many  who  prefer  the  100  inch  range. 
It  is  the  intention  of  the  author  to  give  the  advantages  and 
disadvantages  of  each  pressure  range  in  the  following  para- 
graphs. 

126 


ORIFICE      METER      MEASUREMENT 

The  first  differential  gauge  placed  on  the  market  carried 
a  metallic  spring  instead  of  a  mercury  pot,  and  a  100  inch 
differential  pressure  range.  It  was  generally  conceded  that 
the  100  inch  pressure  range  for  that  type  of  differential  gauge 
was  the  best.  Manufacturers  advised  that  this  type  of 
gauge  gave  best  service  working  at  a  range  from  40  inches 
to  60  inches.  The  range  from  60  inches  to  100  was  only  used 
in  case  of  an  emergency,  or  when  there  was  an  extreme  rise 
in  the  differential  pressure,  in  which  case  the  pressure  range 
above  60  inches  acted  as  a  factor  of  safety  to  the  spring. 

The  mercury  type  of  differential  gauge  superseded  the 
spring  type,  and  in  itself  acts  as  a  safety  valve  to  take  care 
of  any  extreme  rise  of  differential  pressure.  To  illustrate 
this : — 

Take  a  100  inch  differential  spring  type  gauge — should 
the  differential  pressure  increase  to  75  inches,  the  spring 
would  not  be  affected.  Of  course,  this  differential  pressure 
would  mean  a  drop  in  the  pressure  in  the  gas  or  liquid  passing 
through  the  meter  of  about  2%  Ib.  for  small  sizes  of  orifices. 

Should  this  same  rise  in  differential  pressure  occur  with 
a  spring  type  gauge  with  a  pressure  range  of  50  inches,  the 
spring  would  break,  putting  the  gauge  out  of  commission. 

With  the  50  inch  range  of  the  mercury  type  differential 
gauge  in  which  the  mercury  acts  as  a  seal  or  safety  valve, 
the  gauge  would  not  be  injured  by  the  rise  in  pressure  above 
50  inches,  as  the  pen  would  be  checked  at  fifty  inches. 

In  measuring  a  certain  volume  of  gas  where  a  100  inch 
differential  pressure  gauge  is  used,  71  per  cent  of  the  volume 
is  measured  by  the  first  fifty  inches  and  29  per  cent  by  the 
second  50  inches  or  that  part  of  the  range  between  50  inches 
and  100  inches.  However,  the  maximum  capacity  of  a  100 
inch  gauge  is  41  per  cent  greater  than  a  fifty  inch  gauge. 
See  article  on  Capacities,  Page  126. 

When  measuring  fluids  in  high  pressure  lines  where  the  loss 
of  pressure  is  not  an  objectionable  factor,  and  where  large 

127 


ORIFICE      METER      MEASUREMENT 


H  -«. 


tj 


ORIFICE      METER      MEASUREMENT 

capacity  is  desired  a  50  or  100  inch  gauge  should  be  used. 
For  casinghead  gas  and  all  vapors  and  liquids  when  the  line 
pressure  is  less  than  50  Ib.  per  sq.  in.,  gauges  having  a  10  or 
20  inch  maximum  differential  range  should  be  used.  For 
gas  and  air  lines  where  the  pressure  is  nearly  atmospheric, 
a  2  J/2  inch  gauge  will  give  excellent  results  with  an  extremely 
low  friction  loss. 

SPECIAL  TYPES  OF  DIFFERENTIAL  GAUGES 

Differential  Gauge,  2^  inch  Range — This  particular 
type  of  gauge,  which  uses  oil  instead  of  mercury  as  a  seal, 
is  especially  adaptable  for  the  measurement  of  gases  under 
pressures  which  do  not  vary  appreciably  from  the  atmos- 
pheric pressure.  As  noted  on  Page  126  the  range  of  this 
gauge  from  maximum  to  minimum  is  the  same  as  any  dif- 
ferential gauge.  The  great  advantage  in  this  gauge  being 
that  the  pressure  loss  occasioned  at  the  orifice  to  produce  a 
reasonable  reading  is  very  slight,  not  amounting  to  more 
than  one  inch  of  water  pressure  on  the  average. 

Combination  Gauge — Gauges  have  been  placed  on  the 
market  which  have  a  0  to  25  inch  differential  range  or  0  to 
100  inch  differential  range  using  the  same  gauge.  This 
gauge  is  especially  adaptable  to  locations  where  the  flow 
varies  for  certain  periods,  and  where  it  is  undesirable  or 
inadvisable  to  change  the  orifice  in  order  to  obtain  a  reason- 
able reading.  By  using  this  type  of  gauge,  the  operator 
can  increase  the  range  of  the  same  orifice  for  reasonable 
readings  from  3J/2  to  1,  to  7  to  1,  without  any  change  of 
orifice  whatever.  For  instance,  if  for  a  period  of  a  month 
the  hourly  flow  varies  from  100,000  to  350,000  feet  per  hour 
and  during  the  subsequent  month  the  flow  decreases  and 
varies  between  50,000  and  175,000  per  hour,  it  is  possible 
to  make  the  entire  change  in  the  gauge  without  any  change 
of  the  orifice,  thus  eliminating  any  breaking  of  the  line. 

129 


ORIFICE      METER      MEASUREMENT 

This  change  is  made  by  simply  interchanging  the  bushings 
or  plugs  which  are  used  in  the  high  pressure  mercury  cham- 
ber and  thus  decreasing  or  increasing  the  area  of  the  pot. 
The  working  parts  are  not  disturbed  at  all.  A  25  inch 
chart  is  used  when  the  25  inch  bushing  is  in  place,  and  the 
100  inch  chart  is  used  when  the  100  inch  bushing  is  in  place. 
This  type  can  be  used  to  great  advantage  in  measuring  steam, 
water  and  oil  where  by-passes  are  undesirable.  Page  325. 

Indicating  Gauges — Gauges  have  been  designed  which 
have  doors  made  of  one  sheet  of  metal  in  which  a  diagram  is 
placed  under  glass  in  the  section  of  the  door  under  which  the 
differential  pen  arm  moves.  This  diagram  is  slotted  and 
contains  a  scale  between  the  slots  on  which  is  indicated  the 
rate  of  flow  per  hour  corresponding  to  various  pressures. 
The  operator  by  simply  noting  the  static  pressure  at  which 
the  gauge  is  working  and  by  following  the  arc  on  the  diagram 
can  determine  the  flow  per  hour  on  the  scale  reading  over  the 
differential  pen  arm.  These  gauges  indicate  the  rate  of  flow 
within  3  per  cent.  They  are  especially  adaptable  for  those 
locations  where  it  is  desirable  to  change  the  rate  of  flow  by 
increasing  or  decreasing  the  pressure  and  differential.  Due 
to  the  various  State  Regulations,  etc.,  it  is  necessary  to 
draw  at  a  uniform  rate  from  the  wells  and  quite  frequently, 
due  to  the  sudden  increase  in  demand,  it  is  necessary  to  in- 
crease the  rate  of  flow.  The  office  man  simply  tells  the 
field  man  to  increase  the  flow  from  100,000  to  200,000  pro- 
viding the  field  man  has  been  passing  100,000  feet  per  hour 
and  the  field  man  is  able  to  make  this  change  without  any 
calculations  on  his  part  whatever,  simply  by  increasing  the 
pressure  and  differential  and  noting  the  scale  reading  op- 
posite the  differential  pen  arm. 

The  doors  of  the  gauge  are  made  standard  so  that  they 
can  be  used  to  replace  doors  on  other  gauges  now  in  use. 

These  indicating  gauges  are  especially  desirable  for 
measuring  steam  or  oil. 

130 


ORIFICE      METER      MEASUREMENT 


Fig.  58— DIFFERENTIAL  GAUGE   WHICH    INDICATES  RATE  OF  FLOW 

PER  HOUR.       IN    MEASURING    GAS    THE     RESULT    IS   READ    IN 

CUBIC  FEET  PER    HOUR.        THIS    DOES    AWAY     WITH     THE 

NEED  OF  PRESSURE  EXTENSIONS   TO  DETERMINE    THE 

RATE  OF  FLOW.         SEE    PAGE    299. 

Patent  applied  for. 


131 


ORIFICE      METER      MEASUREMENT 

Recording  Differential  and  Static  Pressure  and  Temper- 
ture  Gauge — These  Differential  and  Static  Pressure  Gauges 
are  equipped  with  recording  thermometer  so  that  the  flowing 
temperature  of  the  gas  is  recorded  on  the  same  chart  as  the 
differential  and  static  pressure.  Gauges  of  this  character 
can  be  used  to  advantage  on  large  gas  mains  where  it  is  de- 
sired to  make  a  correction  for  the  amount  of  flowing  gas 
according  to  temperature  of  the  gas.  The  temperature  is 
recorded  inside  of  the  zero  differential  circle  of  the  chart. 
The  benefit  of  having  the  three  records  on  one  chart  is  ob- 
vious. See  Page  234. 

DEVIATION   IN   FLOW  DUE   TO   HIGH   RATIO    OF 
DIFFERENTIAL  TO  PRESSURE 

In  all  of  the  calculations  relative  to  flow  of  fluids  through 
orifices  the  general  formulae  and  expressions  of  flow  have  been 
simplified  and  are  based  on  the  assumption  that  the  difference 
between  the  upstream  pressure  and  the  downstream  pressure 
is  small  when  compared  with  either  the  upstream  or  the  down- 
stream pressure,  or  that  the  ratio  of  the  differential  to  the 
pressure  is  small. 

In  measuring  fluids  which  are  nearly  incompressible, 
such  as  water  or  oil  through  an  orifice  meter,  there  is  practi- 
cally no  change  in  the  density  as  the  fluid  passes  the  orifice. 
The  quantity  is  correctly  represented  by  the  formula  Q  = 
CV  h  when  the  velocity  is  less  than  the  critical  velocity. 

When  measuring  compressible  fluids  ssach  as  air,  natural 
gas,  artifical  gas,  hydrogen,  etc.,  the  density  of  the  fluid  is 
changed.  The  quantity  flowing  is  based  on  the  velocity 
which  is  obtained  by  calculating  the  formula  V  =  Cv^2gH, 
where  H  is  the  differential  expressed  in  feet  head  of  flowing 
fluid.  The  value  of  H  varies  and  depends  on  the  line  pressure. 
Theoretically  it  is  assumed  that  the  line  pressures  at  both 
connections  are  the  same  but  this  is  not  true  due  to  the  dif- 
ferential created  by  the  orifice.  As  the  ratio  of  the  dif- 
ferential to  the  line  pressure  increases,  the  greater  will  be 

132 


ORIFICE      METER      MEASUREMENT 


the  difference  in  values  of  the  differential  in  feet  head  of 
flowing  fluid  when  expressed  in  terms  of  the  upstream  and 
downstream  pressure. 


Velocity  at  Ori- 
fice in  feet  per 
sec. 

Deviation  of  cal- 
culated result, 
from  true  re- 
sult, in    pei- 
cent. 

Velocity  at  Ori- 
fice in  feet  per 
sec. 

Deviation  of  cal- 
culated result, 
from  true  re- 
sult, in    per 
cent 

900 
800 
700 
600 

17.0 
14.8 
12.6 
10.4 

500 
400 
300 

8.2 
6.0 

3.8 

Recently  a  series  of  30  tests  was  conducted  in  which  the 
ratios  of  differential  to  the  downstream  pressure  varied 
from  10  per  cent  to  100  per  cent.  A  holder  was  used  as  a 
standard  of  measurement.  Deviations  in  percentage  of  the 
calculated  volumes,  using  the  published  Coefficients  of  the 
orifices,  from  the  actual  volume  were  plotted  for  two  types 
of  connections,  one  where  pressures  were  obtained  at  pipe 
connections  (static  pressure  at  the  downstream  connection) 
and  the  other  where  the  pressures  were  obtained  at  the  flanges 
(static  pressure  at  the  downstream  connection).  These 
deviations  were  plotted  against  the  actual  velocity  of  the 
air  through  the  orifice  and  indicated  that  the  percentage 
deviation  for  either  of  the  types  of  connections  was  the  same 
for  the  same  rate  of  flow  in  feet  per  second,  being  plus  for 
the  upstream  static  pressure  connection  and  minus  for  the 
downstream  static  connection. 

The  number  of  tests  are  too  meager  to  indicate  or  develop 
a  formula  or  curve  for  a  series  of  mutlipliers  to  be  used  when 
high  ratios  of  differential  to  pressure  exist.  On  account  of 
the  varying  value  of  the  coefficient  of  velocity,  it  is  im- 
possible to  give  definite  factors  from  the  data  obtained  for 
various  ratios  of  diameter  of  orifice  to  diameter  of  pipe. 

All  of  the  published  Coefficients  were  based  upon  experi- 
mental data  obtained  by  using  orifices  in  which  the  ratio  of 

133 


ORIFICE      METER      MEASUREMENT 


-F/pG  Tops  or  connec6/ons- 


r~/ange  Tops  or  Connect; Sons 
/ — -  Or/ free 


H* 


££g*JL —  -*/>/«/ 


m.  of  P/p&  — 


-x?^  ttysipa/st&  i/ne  rr& 

' 


Fig.  59— SKETCH  SHOWING  STREAM  FLOW  THROUGH  AN  ORIFICE 

AND  THE  RELATIVE  STATIC  PRESSURES  AT  VARIOUS  POINTS 

LONGITUDINAL    SCALES    ARE  THE   SAME 


<?  /  <?  ^ 

fJ/amQ£e.r  0f  (Jr/f/cG  /n  fnCf/e-5 
^  60— HOURLY  ORIFICE  COEFFICIENTS  FOR  4  IN-  LINE  FOR  AIR 

134 


ORIFICE      METER      MEASUREMENT 

differential  to  pressure  was  low.  These  Coefficients  should 
be  used  in  a  similar  manner  in  actual  practice  and  should  not 
be  used  under  exceptional  conditions  as  above  indicated 
without  the  use  of  multipliers  or  factors,  which  cannot  be 
furnished  at  present.  It  is  recommended  that  the  reading 
on  the  differential  gauge  in  inches  of  water  should  seldom 
exceed  twice  the  value  of  the  static  pressure  in  pounds  per 
square  inch  absolute  for  any  type  of  connections  in  order  to 
obtain  accurate  results  without  the  use  of  multipliers,  that 
is,  the  average  maximum  differential  pressure  should  not 
exceed,  10  inches  at  20  inches  mercury  vacuum  (5  Ib.  abs.), 
50  inches  at  10  Ib.  (24.4  Ib.  abs.),  etc. 

PRESSURE  CONNECTIONS  OR  TAPS 

When  the  main  pipe  taps  are  made  at  points  2j/^>  diameters 
upstream  and  8  diameters  downstream  from  the  orifice,  these 
connections  are  called  Full  Flow  Connections  and  quite 
frequently  are  known  as  Pipe  Taps.  When  the  taps  for 
the  pressure  connections  are  made  close  to  the  orifice, 
through  the  flanges,  the  taps  are  called  Flange  Taps.  See 
Fig.  59.  In  the  2J/2  and  8  diameter  or  Pipe  Tap  installation, 
the  connections  are  made  at  points  where  the  stream  line 
flow  occupies  the  full  section  of  the  pipe,  hence  the  descriptive 
term  Full  Flow  Connections.  These  points  were  chosen  by 
the  first  experimenters  as  being  the  points  at  which  the 
differential  would  be  approximately  the  least  and  the  most 
consistent  that  could  be  obtained  by  any  combination  of 
points.  In  other  words,  the  line  pressure  at  a  point  2J/2 
diameters  upstream  is  the  least  pressure  that  exists  upstream 
from  the  orifice,  and  the  pressure  at  a  point  8  diameters 
downstream  is  the  greatest  uniform  pressure  which  exists 
below  the  orifice.  The  point  of  maximum  downstream  pres- 
sure is  about  6  diameters  downstream  from  the  orifice. 

Where  the  pressures  are  obtained  at  the  flanges,  the 
upstream  pressure  is  slightly  greater  than  the  minimum 
upstream  pressure,  and  the  pressure  at  the  downstream  con- 

135 


ORIFICE      METER      MEASUREMENT 


nection  is  slightly  greater  than  the  least  downstream  pres- 
sure (in  the  vicinity  of  the  orifice).  The  least  pressure 
(near  the  orifice)  exists  about  ^  of  the  pipe  diameter  down- 
stream from  the  orifice. 

From  the  above  facts  it  follows  that  the  differential 
pressure  between  connections  at  the  flanges  is  always  greater 
for  the  same  velocity  through  the  same  orifice  (See  Fig.  59) 
than  that  obtained  at  the  Pipe  Taps,  (one  connection  2J/2 
diameters  upstream  and  the  other  8  diameters  downstream) . 
In  other  words,  the  differential  obtained  between  taps  at  the 
flanges  is  an  exaggerated  differential. 

When  taps  are  made  in  the  flanges  for  connections  the 
openings  must  be  located  with  precision  as  a  small  variation 
in  the  distance  from  the  flanges  produces  an  appreciable 
change  in  the  differential  due  to  the  fact  that  the  pressure 
varies  at  points  within  J4  of  a  diameter  of  the  orifice.  At 
the  points  for  Full  Flow  Connections  a  variation  of  an  inch 
in  the  location  does  not  produce  a  readable  effect,  for  the 
reason  that  the  pressures  at  these  points  and  at  points  within 
a  diameter  in  either  direction  are  steady  and  do  not  vary 
appreciably. 

Friction  Loss — The  following  Table  gives  the  percentages 
of  friction  loss  to  total  differential  for  Full  Flow  and  Flange 
Connections  for  various  ratios  of  orifice  to  size  of  pipe. 

Table  23 
Percentage  of  Friction  Loss  to  Differential 


Ratio  X 

Full  Flow  Con- 

Flange Connec- 

v       Diameter  of  Orifice 

nections  Per 
Cent  Loss 

tions  Per  Cent 
Loss 

Diameter  of  Pipe 

.15 

100 

96 

.30 

100 

89 

.45 

100 

75 

.60 

92 

57 

.75 

80 

40 

136 


ORIFICE      METER      MEASUREMENT 


137 


ORIFICE      METER      MEASUREMENT 

The  friction  losfe  at  a  2%  inch  orifice  in  a  6  inch  line  for  a 
50  inch  differential  reading  is  100  per  cent  or  50  inches  with 
Full  Flow  Connections,  and  38  inches  when  the  same  dif- 
ferential is  obtained  when  using  the  same  orifice  with  Flange 
Connections.  If  a  4J^  inch  orifice  is  used  in  a  6  inch  pipe  the 
friction  loss  at  50  inch  differential  reading  is  40  inches,  and 
20  inches  for  the  Full  Flow  Connections  and  Flange  Con- 
nections respectively.  This  relation  may  be  expressed  as 
follows.  With  Full  Flow  Connections  the  differential  is  1J4 
times  the  friction  loss  and  with  Flange  Connections  the 
differential  is  2^  times  the  friction  loss  at  an  orifice  which  is 
%  of  the  diameter  of  the  pipe.  It  is  noted  that  the  friction 
loss  percentage  decreases  as  the  size  of  the  orifice  increases. 

At  a  first  glance  it  would  seem  that  the  Flange  Con- 
nections are  preferable,  but  it  is  a  self  evident  fact  that  with 
a  definite  rate  of  flow  through  an  orifice  the  friction  loss  will 
be  the  same  as  long  as  the  same  orifice  is  used  in  the  same 
pipe.  The  loss  does  not  depend  on  whether  the  pressures  are 
obtained  at  a  mile  away  on  each  side  of  the  orifice  or  within 
H  inch. 

Table  23  does  not  tell  the  whole  story  for  it  does 
not  take  into  consideration  the  larger  value  of  the  coeffi- 
cient for  the  Full  Flow  Connections  when  using  the  same  size 
of  orifice  in  the  same  pipe.  See  Fig.  60. 

In  Table  24  it  is  shown  that  for  the  same  size  of 
orifice  the  Hourly  Orifice  Coefficient  for  Pipe  Tap  connections 
is  always  greater  than  the  Hourly  Orifice  Coefficient  for 
Flange  Tap  connections  and  that  for  the  larger  sizes  of  ori- 
fices the  Pipe  Tap  coefficient  becomes  considerably  greater 
than  the  Flange  Tap  coefficient.  In  order  to  indicate  the 
same  flow  the  differential  reading  on  the  chart  of  the  gauge 
attached  to  the  flange  taps  reaches  its  maximum  limit 
(20  inches) ,  when  the  pen  of  the  other  gauge  is  registering  at 
one-half  of  its  maximum  range,  (10  inches).  The  friction 
loss  in  each  case  is  the  same  for  the  same  flow. 

138 


ORIFICE      METER      MEASUREMENT 


Table  24 

Comparison  between  two  20  inch  Differential  Gauges,  measuring 
the  same  flow  through  the  same  orifice  (one  with  Pipe  Tap  connections 
and  the  other  with  pressure  connections  at  the  flanges)  when  the 
gauge  connected  to  the  Pipe  Taps  is  indicating  a  10  inch  reading. 


Gauge  with  Connections 

Gauge  with  Connections 

Dia- 

at Pipe  Taps 

at  Flange  Taps 

meter 
of  Ori- 
fice 

Quan- 
tity 

Coeffi- 

Chart 
Read- 

Fric- 
tion 
Loss 

Coeffi- 

Chart 
Read- 

Fric- 
tion 
Loss 

Inches 

cient 

ing 
Inches 

Inches 

cient 

ing 
Inches 

Inches 

of  Water 

of 
Water 

of  Water 

of 
Water 

*A 

836 

83.6 

10 

10 

81.8 

10.5 

10 

IK 

3506 

350.6 

10 

10 

327.4 

11.5 

10 

1% 

7382 

738.2 

10 

10 

642.5 

13.2 

10 

21A 

18562 

1856.2 

10 

9 

1429.8 

16.8 

9 

3 

32962 

3296.2 

10 

8 

2322.7 

20.0 

8 

Size  of  Pipe  4.026  inches.       Pressure  10  Ib.  absolute. 
Air  being  measured. 

Table  25 

Comparing  two  50  inch  gauges,  one  with  Full  Flow  Connections 
and  the  other  with  Flange  Connections  each  indicating  a  differ- 
ential of  25  inches,  (except  as  noted).  Size  of  Pipe  4  inches.  Air 
being  Measured.  Pressure  16  Ib.  Absolute. 


Full  Flow  Connections 


Flange  Connections 


Dia- 
meter 
of 
Orifice 
Inches 

Hourly 
Orifice 
Coeffi- 
cient 

Quan- 
tity 
cu.    ft. 
per 
hour 

Fric- 
tion 
Loss 
Inches 
Water 

Dia- 
meter 
of 
Orifice 
Inches 

Hourly 
Orifice 
Coeffi- 
cient 

Quan- 
tity 
cu.  ft. 
per 
hour 

Fric- 
tion 
Loss 
Inches 
Water 

H 

83.6 

1672 

25 

% 

81.8 

1636 

24 

IK 

350.6 

7012 

25 

IK 

327.4 

6548 

22 

IK 

738.2 

14764 

25 

IK 

642.5 

12850 

19 

2}/2 

1856.2 

37124 

23 

V/2 

1429.8 

28596 

14 

2^ 

2481.9 

49638 

21 

3 

2322.7 

46454 

10 

3 

3296.2 

65924 

20 

3 

2322.7 

65690* 

20 

*At  50  inches  differential 


139 


ORIFICE      METER      MEASUREMENT 


In  Table  25  it  is  shown  that  for  various  quantities  of 
gas  passing  the  same  orifice  at  the  same  differential,  the 
friction  loss  is  less  for  Flange  Connections  but  the  quan- 
tity is  also  less,  also  that  in  order  to  measure  the  same  maxi- 
mum quantity  that  the  gauge  with  Full  Flow  Connections 
measures  at  a  25  inch  reading,  the  gauge  with  Flange  Con- 
nections must  indicate  at  the  limit  of  the  chart  in  which 
case  the  pressure  loss  is  the  same. 

The  following  table  shows  very  clearly  that  a  gauge  of  a 
certain  maximum  range  with  Full  Flow  Connections  will 
measure  the  same  or  slightly  greater  quantities  at  the  same 
relative  chart  reading  with  a  less  friction  loss  than  a  gauge 
of  double  its  maximum  range  with  Flange  Connections. 

Table  26 

Comparison  between  a  50  inch  gauge  with  2J/2  and  8  diameter 
connections  and  a  100  inch  gauge  with  Flange  Connections,  each 
gauge  indicating  a  differential  equal  to  }/£  of  its  maximum  differential 
range.  Size  of  Pipe  4  inches.  Air  being  measured.  Pressure  50  Ib. 
absolute. 


50  in.  Gauge,  Full  Flow 
Connections 


100  in.  Gauge,  Flange  Con- 
nections 


Dia- 
meter 
of 
Orifice 
Inches 

Hourly 
Orifice 
Coeffi- 
cient 

Quan- 
tity cu. 
ft.  per 
Hour 

Fric- 
tion 
Loss 
Inches 
Water 

Dia- 
meter 
of 
Orifice 
Inches 

Hourly 
Orifice 
Coeffi- 
cient 

Quan- 
tity cu. 
ft.  per 
Hour 

Fric- 
tion 
Loss 
Inches 
Water 

H 

121.1 

4284 

25 

H 

81.84 

4092 

48 

V4 

519.9 

18390 

25 

1M 

327.4 

16370 

44 

2 

1019.4 

36070 

25 

m 

642.5 

32130 

38 

2% 

2146.8 

76070 

22 

&A 

1429.8 

71500 

27 

3 

3296.2 

116620 

20 

3 

2322.7 

116100 

20 

It  is  noted  that  a  50  inch  gauge  at  the  maximum  size  of 
orifice  with  Full  Flow  Connections  has  approximately  the 
same  capacity  as  a  100  inch  gauge  with  Flange  Connections. 
These  ratios  and  percentages  are  true  for  the  same  relative 
capacities  of  gauges. 

140 


ORIFICE      METER      MEASUREMENT 

Considerable  has  been  said  in  regard  to  the  merits  of  both 
types  of  connections  relative  to  friction  loss,  capacities,  etc., 
but  the  gist  of  the  facts  is  as  follows.  The  Flange  Connections 
are  more  compact;  the  gauges  indicate  a  higher  differential 
for  the  same  flow  through  the  same  orifice ;  the  taps  must  be 
located  with  greater  precision.  Full  Flow  (Pipe  Tap)  Con- 
nections are  located  at  points  where  the  pressures  are  uni- 
form and  steady;  the  range  of  capacity  is  41  per  cent  greater 
from  minimum  to  maximum  size  of  orifice  for  the  same  pipe ; 
the  gauges  indicate  a  lower  differential,  requiring  a  smaller 
maximum  range  of  gauge  for  the  same  flow. 

Friction  loss  depends  solely  on  the  rates  of  flow,  size  of 
orifice  and  size  of  pipe.  The  larger  the  orifice  the  less  the 
friction  loss  which  in  turn  means  a  lower  differential  and  a 
gauge  of  low  maximum  range  regardless  of  the  type  of  con- 
nections. 

PRESSURE  LOSS 

Whenever  an  orifice  is  placed  in  a  line  a  loss  of  pressure 
is  created.  This  loss  varies  from  40  to  100  per  cent  of  the 
differential  reading  (See  Page  136)  on  the  chart.  For  in- 
stance, if  the  differential  reading  is  54  inches  the  loss  in  pres- 
sure is  not  less  than  21  inches  of  water  or  0.8  Ib.  and  may 
amount  to  54  inches  of  water  or  2  Ib.  through  the  orifice  de- 
pending on  the  location  of  the  pressure  connections  and  the 
size  of  orifice.  As  the  size  of  the  orifice  increases  the  pro- 
portion of  pressure  loss  due  to  friction  compared  to  differential 
reading  becomes  less.  For  smaller  sizes  of  orifices  the  lost 
head  is  equal  or  nearly  equal  to  the  differential  pressure. 
On  a  vacuum  line  this  loss  creates  a  less  vacuum  at  the  well  if 
the  meter  is  placed  between  the  pump  and  the  well.  Each 
13.6  inches  of  water  pressure  amounts  to  1  inch  of  mercury 
vacuum.  For  example,  if  a  vacuum  pump  pulling  26  inches 
of  vacuum  is  placed  on  a  line  and  the  normal  pressure  loss 
through  the  line  without  an  orifice  is  4  inches  of  mercury 
head,  the  vacuum  at  the  well  would  be  22  inches.  If  a 

141 


ORIFICE      METER      MEASUREMENT 

small  orifice  is  placed  in  this  line  and  the  differential  gauge 
reading  is  54  inches  of  water  (approximately  4  inches  of  mer- 
cury head)  then  the  vacuum  existing  at  the  well  is  only  18 
inches.  In  this  case  it  will  be  noted  that  the  orifice  creates 
as  much  friction  loss  as  the  pipe  line  itself. 

To  overcome  this  difficulty  differential  gauges  having  a 
maximum  reading  of  10  and  20  inches  have  been  placed  on 
the  market.  By  using  meters  of  these  lower  ranges  the  size 
of  the  orifice  is  increased,  thereby  decreasing  the  total  dif- 
ferential pressure  required  to  obtain  an  accurate  reading. 
The  proportionate  friction  loss  as  compared  with  the  dif- 
ferential reading  is  likewise  decreased. 

The  use  of  orifice  meters  having  a  differential  range  of 
from  60  to  100  inches  on  vacuum  lines  should  be  discouraged 
on  account  of  the  friction  losses  above  stated.  Any  dif- 
ferential gauge  having  a  range  from  0  to  10  inches  or  greater, 
will  have  a  capacity  sufficient  to  measure  the  flow  through  any 
vacuum  line.  The  maximum  capacity  of  a  10  inch  differential 
gauge  is  32  per  cent  of  the  maximum  capacity  of  a  100  inch 
gauge  and  71  per  cent  of  the  maximum  capacity  of  the  20 
inch  gauge.  However,  the  friction  loss  in  measuring  the 
same  quantity  of  gas  at  the  same  relative  reading  on  the  10 
inch  differential  gauge  chart  is  less  than  10  per  cent  of  the 
friction  loss  occasioned  by  using  a  100  inch  gauge  and  less  than 
50  per  cent  of  that  for  a  20  inch  gauge.  For  instance,  in 
the  previous  example  with  a  10  inch  gauge  at  the  same  rela- 
tive chart  reading  of  5.6  inches  the  friction  loss  would  be 
less  than  5.6  inches  of  water  pressure  or  0.4  inches  of  mercury 
head  which  would  leave  a  vacuum  of  21.6  inches  at  the  well 
with  26  inches  at  the  pump,  a  line  loss  of  4  inches  mercury 
head  and  a  meter  loss  of  .4  inches  of  mercury.  Although  it 
is  possible  to  obtain  low  readings  from  differential  gauges 
having  the  higher  ranges  the  same  percentage  of  accuracy  in 
reading  cannot  be  obtained,  as  when  using  gauges  of  lower 
maximum  ranges.  For  instance,  the  closest  reasonable 

142 


ORIFICE      METER      MEASUREMENT 

reading  which  could  be  obtained  on  a  100  inch  chart  is 
about  ^/2  of  an  inch.  The  error  for  a  2  inch  differential 
reading  will  amount  to  12  per  cent,  whereas,  on  a  10  inch 
chart  it  is  easily  possible  to  obtain  readings  within  .05  inch, 
which  would  amount  to  1J4  per  cent  deviation  for  a  2  inch 
differential  reading.  (See  Page  126). 

PULSATING  FLOW 

A  great  many  people  believe  that  when  they  have  a  pul- 
sating volume  of  gas  or  liquid  to  be  measured,  it  is  only 
necessary  to  install  "deadeners"  or  pinch  valves  on  gauge 
lines  to  the  differential  gauge  in  order  to  obtain  accuracy. 
This  is  erroneous.  Simply  because  one  kills  the  pulsation 
in  the  lines  leading  to  the  high  and  low  pressure  side  of  the 
differential  gauge  does  not  mean  that  they  have  stopped  the 
pulsation  of  the  fluid  passing  through  the  orifice.  It  is  not 
practicable  to  measure  pulsating  flow  by  either  one  orifice 
meter  or  a  displacement  meter.  It  is  as  unreasonable  as  to 
attempt  to  weigh  a  person  jumping  around  on  a  penny-in- 
the-slot  weighing  machine. 

The  problem  which  has  proven  most  puzzling  has  been 
the  measurement  of  a  pulsating  flow.  This  is  particularly 
true  where  the  pulsations  are  rhythmic,  as  in  the  vicinity  of 
compressor  stations  with  reciprocating  compressor  pistons. 
The  following  statement  illustrates  the  varying  results  ob- 
tained in  measuring  gas  where  the  pulsations  were  produced 
by  compressors.  An  orifice  meter  early  installed  at  such  a 
location  failed  to  check  with  the  station  or  with  meters  some 
17  miles  away  on  the  same  line.  In  endeavoring  to  locate 
the  difficulty,  a  series  of  recording  gauges  was  installed,  both 
with  and  without  devices  for  "deadening"  the  pulsations 
in  the  lines  leading  to  the  gauges.  Finally  a  spring  recording 
gauge,  a  mercury  float  gauge  of  the  type  originally  installed, 
a  differential  recording  gauge,  and  a  water  U  tube,  were  con- 
nected in  parallel.  These  gauges  were  all  calibrated  in 

143 


ORIFICE      METER      MEASUREMENT 

unison,  and  agreed  very  well  under  conditions  of  steady  flow. 
When  the  compressor  station  was  started,  the  gauges  took 
widely  varying  positions;  some  dropped  down  to  half  their 
former  reading,  despite  the  increased  flow,  one  took  a  nega- 
tive reading  as  though  the  flow  were  reversed  and  the  water 
column  took  a  wholly  indeterminate  condition  of  churned 
foam ;  some  of  the  gauges  moved  about  in  an  erratic  way  and 
others  gave  steady  indications,  but  wholly  unrelated  to  the 
quantity  of  gas.  A  proportional  meter  installed  in  tandem 
at  this  point  gave,  over  a  period  of  months,  a  record  erratic 
and  irreconcilable  as  compared  with  pump  station  displace- 
ment, line  flow  formula,  or  meters  17  miles  away  operating  on 
the  same  gas  with  steady  flow. 

Similar  disturbances  in  the  accuracy  of  the  record  are 
occasioned  by  irregular  pulsations  occasioned  by  the  action 
of  fluid  in  the  line.  Disturbances  are  particularly  serious 
when  occasioned  by  irregular  or  imperfect  action  of  auto- 
matic pressure  regulators  in  the  vicinity  of  the  meter. 
One  attempt  was  made  where  a  device  was  installed  ahead 
of  a  compressor  station  with  the  idea  of  dividing  the  gas  into 
about  20  different  streams  and  making  each  stream  traverse 
a  path  of  different  length  so  that  the  wave  motion  from 
different  parts  of  the  cycle  would  be  made  to  interfere  at 
the  point  where  the  gas  was  again  brought  to  a  common 
line.  This  was  almost  successful,  and  it  is  believed  that  by 
a  little  further  calculation  and  change  of  arrangement  to 
secure  more  perfect  interference  a  measurement  at  this  point 
may  be  secured. 

Pulsations  due  to  fluid  and  imperfect  regulators  are 
obviously  questions  of  simple  correction,  by  separators,  drips 
and  mechanical  repairs. 

To  obtain  accuracy  where  the  gas  pulsates  badly,  one 
should  eliminate  the  pulsation  or  move  the  orifice  meter  to  an- 
other location.  To  eliminate  pulsation  it  is  necessary  to  install 
drip  tanks  or  more  pipe  area  on  the  inlet  side  of  the  meter. 

144 


ORIFICE      METER      MEASUREMENT 

Compressors  are  the  greatest  producers  of  pulsation. 
Regulators,  and  gates  near  the  meter,  and  water  or  oil  in  a 
gas  line  will  also  create  pulsation  in  the  line. 

Where  pulsation  is  caused  by  regulators  or  fittings  it  is 
not  a  difficult  matter  to  move  the  regulators  or  fittings  far 
enough  back  of  the  meter  so  as  not  to  cause  counter  currents, 
eddies,  or  pulsations. 

Of  course,  a  very  slight  pulsation  may  not  have  any  ma- 
terial effect  on  the  accuracy  of  the  orifice  meter,  but  it  is  best 
to  have  none. 

Pulsation  and  Vibration — In  order  to  cover  this  subject 
thoroughly  a  distinction  must  be  made  between  a  vibrating 
differential  pen  arm  and  the  pulsating  flow  which  occurs 
through  the  orifice. 

The  differential  pen  arm  will  vibrate  due  to  several  causes 
such  as;  intermittent  flow  from  a  well,  varying  speed  of  a. 
compressor  or  pump,  non-uniform  consumption  by  a  drilling 
boiler,  etc.  In  these  cases  the  change  in  the  rate  of  flow  is 
slow  enough  to  permit  the  differential  pen  arm  to  entirely  or 
partially  record  the  changes. 

The  pulsation  which  is  produced  by  the  rapidly  changing 
rate  of  flow  due  to  a  compressor  or  pump,  is  usually  so  rapid 
that  the  differential  pen  arm  indicates  a  uniform  smooth 
record  which  may  be  greatly  in  error  depending  entirely 
upon  the  character  of  the  wave  motion. 

Vibration  of  Differential  Pen  Arm — In  endeavoring  to  de- 
crease the  vibration  of  the  differential  pen  arm,  the  use  of 
washers  or  the  method  of  partially  closing  valves  on  the  gauge 
lines,  is  not  satisfactory  as  any  very  small  leaks  between  the 
valves  and  the  gauge  will  produce  an  erroneous  reading. 
Washers  may  become  partially  stopped  up  and  actually  pre- 
vent the  full  pressure  at  the  connection  from  being  exerted  on 
the  mercury.  Where  it  is  impossible  to  place  large  chambers 
or  reservoirs  in  the  main  line  to  eliminate  the  vibration,  the 
vibration  can  be  reduced  most  satisfactorily  when  the  dif- 

145 


ORIFICE      METER      MEASUREMENT 

f  erential  gauges  are  equipped  with  small  bushings  which  re- 
tard the  flow  of  mercury  from  the  high  pressure  portion  of  the 
gauge  to  the  low  pressure  portion  of  the  gauge,  or  vice  versa. 
By  using  these  bushings  it  is  possible  to  automatically  aver- 
age the  peaks  and  hollows  of  the  differential  reading,  in  cases 
of  wells  which  flow  by  heads  or  where  a  well  is  supplying  fuel 
to  a  drilling  boiler  or  any  machine  at  which  the  consumption 
of  fuel  is  intermittent,  and  thereby  reduce  the  time  required  in 
the  office  to  estimate  the  average  reading.  Bushings  in- 
stalled in  the  mercury  columns  do  not  increase  the  accuracy 
of  the  gauge  and  do  not  decrease  it  except  where  the  move- 
ment of  the  differential  pen  arm  is  greatly  retarded  requiring 
more  than  three  minutes  to  cover  the  range  of  the  chart. 
The  results  obtained  from  charts  where  the  differential 
record  is  averaged  in  this  way  will  be  the  same  as  would 
be  obtained  by  averaging  each  15  minute  period  by  in- 
spection. 

Bven  though  the  vibration  is  eliminated,  pulsation  may 
exist  and  the  layout  should  be  tested  as  prescribed  in  the 
following  article  if  there  is  a  possibility  of  error  due  to 
rhythmic  pulsation  through  the  orifice.  It  is  almost  a 
certainty  that  the  differential  reading  is  erroneous  if  the 
static  pen  arm  vibrates  rapidly. 

Pulsation — As  an  example  of  the  excessive  effect  the  pul- 
sation due  to  very  rapid  uniformly  changing  rates  of  flow  may 
have  upon  results,  we  show  in  Fig.  62,  layout  of  the  piping  in 
which  an  orifice  meter  was  installed  for  measurement  of 
steam.  Fig.  63  is  a  chart  obtained  while  conducting  some 
tests  for  measurement  of  steam.  It  will  be  noticed  in  Fig.  62 
that  the  steam  header  contained  two  connections  to  machines 
using  steam,  one  an  air  compressor  and  the  other  a  generator. 
Some  of  the  steam  after  passing  by  these  connections  was 
measured  by  an  orifice  meter  A  and  subsequently  weighed  as 
condensate.  The  flow  of  steam  through  the  orifice  meter  A 
was  regulated  by  a  valve  C  on  the  line  just  prior  to  conden- 

146 


ORIFICE      METER      MEASUREMENT 

sation  of  the  steam.  The  clock  on  the  differential  gauge  was 
altered  so  that  it  made  a  revolution  in  approximately  96 
minutes,  therefore,  the  chart  Fig.  63  moved  about  15  times 
as  fast  as  an  ordinary  24  hour  chart. 

Whenever  the  valve  C  was  opened  for  a  certain  number  of 
turns  and  left  in  that  position,  it  was  noticed  in  all  instances 
that  the  rate  of  flow  was  uniform.  On  the  chart  shown  in 
Fig.  63,  valve  C  was  partially  opened  during  a  period  when 
both  the  generator  and  compressor  were  shut  down,  and  if 
they  had  remained  so  the  reading  would  have  continued 
uniform  corresponding  to  a  differential  of  16  inches.  Bight 
minutes  after  valve  C  was  opened  the  generator  was  started 
and  the  differential  increased  from  16  inches  to  30  inches 
without  any  change  in  the  valve  C,  consequently  without 
any  increase  whatever  in  the  amount  of  steam  passing  through 
the  orifice.  After  the  compressor  was  started  the  differential 
reading  again  increased  without  any  increase  in  the  amount 
of  steam  passing  through  the  orifice.  Inasmuch  as  the  in- 
crease of  differential  was  not  due  to  an  increased  flow  of 
steam,  the  effect  was  due  to  the  pulsation  occasioned  by  the 
opening  and  closing  of  the  slide  valves  of  the  generator  and 
compressor,  both  of  them  being  reciprocating  units.  It  is 
noted  that  prior  to  the  test  when  the  machines  were  not 
operating  that  the  differential  arm  remained  at  zero  when 
there  was  no  steam  passing  through  the  orifice,  and  that 
after  valve  C  was  closed,  when  there  was  no  steam  passing 
through  the  orifice,  that  a  differential  pressure  of  approxi- 
mately 9  inches  of  water  was  recorded,  due  to  pulsation 
only.  This  differential  continued  as  long  as  the  generator 
and  compressor  operated  at  a  uniform  speed. 

The  static  pen  arm  in  previous  tests  vibrated  over  a 
range  of  10  to  15  Ib.  with  a  frequency  of  the  opening  and 
closing  of  the  valves  of  the  reciprocating  units  when  they 
were  operating.  To  lessen  this  vibration  a  dash  pot  was 
attached  to  a  static  pen  arm  producing  the  smooth  lines  as 

147 


ORIFICE      METER      MEASUREMENT 

shown.  The  effect  of  partially  closing  the  valves  on  the 
gauge  lines  also  produced  a  smooth  pressure  reading  but  gave 
erratic  differential  readings.  In  all  cases  when  the  gauge 
line  valves  were  fully  opened  the  differential  reading  was 
very  uniform  without  any  appreciable  vibration. 

The  weight  of  steam  passing  the  orifice  checked  with  a 
differential  reading  of  16  inches  for  the  total  period  of  the 
test,  so  that  the  flow  corresponded  to  the  reading  obtained 
before  the  pulsation  occurred.  The  differential  due  to 
pulsation  caused  by  the  two  machines,  was  9  inches ;  and  the 
differential  due  to  pulsation  and  flow  was  49  inches.  As- 
suming the  pressure  as  85.6  lb.,  atmospheric  pressure  14.4 
and  Hourly  Orifice  Coefficient  as  10,  the  rate  of  flow  due  to 
the  differential  of  16  inches  was  400  lb.  per  hour.  (10V100X16 
=  400).  The  flow  corresponding  to  a  9  inch  differential 
would  be  300  lb.  per  hour  (10V  100X9  =  300).  For  a  49 
inch  differential  the  corresponding  rate  of  flow  would  be  700 
lb.  per  hour.  Therefore,  the  effects  due  to  a  pulsation 
reading  of  9  inches  increased  the  flow  reading  from  16  inches 
to  a  combined  reading  of  49  inches,  not  simply  an  addition, 
but  a  total  reading  which  was  equivalent  to  the  reading 
which  would  be  obtained  by  the  sum  of  combined  theoretical 
flows  which  would  have  existed  for  the  two  independent 
readings,  flow  and  pulsation  (400+300  =  700).  With  this 
layout  the  effect  of  the  pulsation  produced  a  reading  equal 
to  the  square  of  the  sum  of  the  square  root  of  the  flow  dif- 
ferential plus  the  square  root  of  the  pulsation  differential. 
[49=  (Vl6+V¥)2=(4+3)2]. 

A  joint  of  pipe  MN  was  then  connected  with  the  main 
ahead  of  the  orifice.  This  pipe  was  closed  at  the  end  and  an 
orifice  B  of  the  same  size  as  the  orifice  in  the  main  was  in- 
serted in  the  line  at  the  same  distance  from  the  junction  of 
the  two  pipes  as  orifice  A.  The  differential  produced  by  the 
pulsation  at  orifice  B  was  the  same  as  at  the  orifice  A  without 
any  flow  through  the  orifices  on  either  line.  Furthermore, 

148 


ORIFICE      METER      MEASUREMENT 


Steam  Header 


Fig. 


ORIFICE      METER      MEASUREMENT 

the  flow  through  the  orifice  A  was  equal  to  the  difference  of 
the  flows,  as  would  be  calculated  from  the  two  charts,  the 
steam  flowing  through  the  orifice  A  producing  a  reading  due 
to  flow  plus  pulsation,  and  the  orifice  C  on  the  dead  line 
producing  a  reading  due  to  pulsation  only. 

In  the  layout  above  described  the  differential  produced 
by  the  pulsation  only  was  the  same  for  the  same  ratio  of 
orifice  to  size  of  pipe,  i.  e.,  a  one-half  inch  orifice  in  a  two  inch 
pipe  produced  the  same  pulsation  differential  as  a  one  inch 
orifice  in  a  four  inch  pipe. 

The  above  remarks  are  the  summarized  results  of  more 
than  sixty  tests  in  which  the  sizes  of  pipes,  orifices  and  rates 
of  flow  were  varied  in  which  the  length  of  straight  pipe  on 
each  side  of  the  orifice  was  16  diameters  or  greater.  The 
effect  of  shorter  lengths  were  not  determined. 

Gauges  may  be  checked  to  determine  if  the  pulsation 
has  any  serious  effect  on  the  registration  by  closing  the  down- 
stream main  valve  in  a  layout  similar  to  Fig.  93,  permitting 
the  gas  to  pass  through  the  by-pass  and  noting  whether  the 
differential  chart  shows  a  reading  when  there  is  no  flow 
through  the  orifice.  If  there  is  a  reading  and  the  valve  is  in 
good  condition  it  indicates  the  flow  calculated  from  the  dif- 
ferential reading  is  in  error. 

If  the  differential  corresponding  to  a  certain  flow  is  9 
inches  and  the  differential  caused  by  pulsation  is  }/±  inch  the 
differential  created  by  the  combined  effect  may  be  12.25 
inches  (V~9~  +  V^25)2  or  6.25  inches  (V~9—  V.~25)  since  the 
effect  of  the  pulsation  may  decrease  the  reading  as  well  as 
increase  it,  depending  on  the  layout. 

The  use  of  two  meters  offers  a  solution  for  those  locations 
where  it  is  impossible  to  install  reservoirs  or  to  locate  the 
meters  so  that  the  effect  of  the  pulsation  can  be  eliminated; 
one  of  the  gauges  being  installed  on  the  main,  recording  the 
differential  produced  by  the  flow  and  pulsation,  and  the  other 

150 


ORIFICE      METER      MEASUREMENT 

meter  on  a  dead  line  registering  the  imaginary  flow  due  to 
pulsation.  The  difference  between  the  results  calculated 
from  these  charts  being  the  true  flow. 

From  the  above  it  is  seen  that  bushings  will  not  produce 
an  accurate  indication  of  the  flow  even  though  the  recorded 
differential  line  is  a  smooth  line,  when  the  static  pressure 
varies  uniformly  and  rapidly  for  the  reason  that  sufficient 
time  may  not  elapse  between  the  periods  of  increased  pressure 
or  decreased  pressure  for  the  differential  pen  arm  to  assume 
a  reading  corresponding  to  the  average  flow.  There  is  only 
one  way  to  take  care  of  a  situation  of  this  kind  with  one 
orifice  and  that  is  to  place  a  deadener  or  reservoir  in  a  main 
gas  line  large  enough  to  absorb  the  shocks  and  cause  a  steady 
flow  from  the  deadener  or  reservoir. 

There  is  no  set  rule  to  follow  that  the  writer  knows  of  in 
regard  to  when  and  when  not  to  install  a  meter  where  the 
flow  is  pulsating.  It  might  be  said  that  in  any  installation 
where  the  static  pressure  pen  arm  does  not  vibrate  that  the 
resultant  reading  obtained  may  be  correct.  It  is  certain 
that  if  the  static  pen  arm  does  vibrate  the  differential  read- 
ing will  be  in  error,  probably  as  much  as  1000  per  cent. 


Fig.  64 — FLANGE  TAP  CONNECTIONS 

151 


ORIFICE      METER      MEASUREMENT 

INSTRUCTIONS  TO  METER  ATTENDANTS 

One  of  our  most  important  operations  is  the  measure- 
ment of  gas,  and  it  is  essential  that  meter  charts  and  records 
reach  the  Chart  Department  in  the  best  possible  condition. 
A  little  -more  attention  and  care  on  your  part  can  prevent  a 
great  many  errors  that  may  not  be  noticed  by  the  one  cal- 
culating the  charts  who  is  not  familiar  with  local  operations. 
You  are  responsible  for  the  condition  of  your  charts  and  we 
wish  to  call  your  attention  to  the  following  points  in  order 
that  you  may  be  properly  instructed.  No  doubt  you  are 
now  observing  many  of  these  points,  but  if  they  are  carried 
out  in  the  following  order,  uniform  methods  will  result  in 
better  charts. 

Changing  Orifice  Meter  Charts — Make  a  zero  differential 
check  and  wait  a  few  minutes  to  see  that  the  pen  remains 
on  the  zero  line,  if  it  does  not,  report  at  once  or  adjust  and 
make  note  of  findings.  Release  pens  from  chart  by  means  of 
pen  lifter,  remove  center  nut  and  slip  chart  off  without 
touching  pens.  Wind  the  clock  and  put  on  new  chart  im- 
mediately, seeing  that  the  chart  is  properly  centered  and  that 
the  differential  or  red  ink  pen  is  on  the  correct  time  line. 
Hold  chart  in  place  and  tighten  chart  nut.  Blot  the  re- 
moved chart  carefully  and  fill  in  complete  information: 
Name  of  Meter,  Location,  Disc  Number,  actual  time  and 
date  chart  was  put  on  and  removed.  Always  sign  your 
name  in  full.  Never  turn  chart  by  hand  to  fill  in  record 
and  make  it  appear  complete  when  such  is  not  the  case. 
Never  allow  24  hour  charts  to  run  for  more  than  one  day, 
except  in  case  of  absolute  necessity,  and  when  this  does  occur, 
make  notes  on  chart  to  identify  corresponding  lines  of  each 
day.  DO  NOT  SAVE  CHARTS  UP  FOR  SEVERAL 
DAYS,  BUT  MAIL  THEM  IN  PROMPTLY  EACH  DAY. 
When  charts,  envelopes  or  other  supplies  are  needed,  make 
request  on  face  of  chart,  and  give  name  and  address  for 
mailing.  Do  not  allow  your  supplies  to  run  out. 

152 


ORIFICE      METER      MEASUREMENT 

When  inking  pens,  use  just  enough  ink  to  fill  the  pen, 
being  careful  not  to  confuse  the  colors.  Always  use  red  ink 
in  the  long  or  differential  pen.  Do  not  allow  excess  ink  to 
run  down  the  pen  arms  or  accumulate  on  the  pen  lifter  where 
it  will  smear  chart.  See  that  the  pens  make  a  good  clear 
line,  and  that  the  colors  do  not  get  mixed.  Pens  should  be 
cleaned  occasionally  to  prevent  deposits  of  dried  ink  and 
dust. 

Before  leaving  meter,  make  sure  that  the  pens  are  touch- 
ing the  chart  and  marking  properly.  Also,  that  the  chart  is 
securely  clamped  and  turning  with  the  clock.  Waiting  a 
few  minutes  after  the  chart  is  changed  and  observing  these 
conditions  will  save  a  great  deal  of  trouble  and  bad  measure- 
ment. See  that  the  gauge  is  protected  from  wind  and  rain, 
and  if  you  are  unable  to  protect  it,  call  attention  to  the  mat- 
ter by  a  note  on  the  chart. 

When  unusual  conditions  are  indicated  by  the  chart, 
determine  the  cause,  if  possible,  and  give  full  information. 
In  case  the  pens  get  off  the  chart,  notify  the  nearest  man  in 
charge  by  telephone,  as  soon  as  possible.  Do  not  allow 
gauge  to  remain  out  of  repair  WITHOUT  CALLING  AT- 
TENTION TO  IT. 

On  all  other  meters  same  care  should  be  given  to  charts. 
Check  readings  on  index  carefully  and  make  subtraction  to 
get  last  delivery.  If  no  delivery  is  shown,  find  the  reason 
and  note  same  on  chart. 

Any  suggestions  for  improvement  that  may  occur  to 
you  will  be  welcomed  in  the  form  of  a  letter. 


Meter  Dept. 
153 


ORIFICE      METER      MEASUREMENT 


TESTING  APPARATUS 
Inspector's  Test  Pump  for  Static  Pressure  Gauges 


Fig. 


Fig.  65  illustrates  an  inspector's  test  gauge  and  pump 
with  carrying  case.  The  use  of  a  test  gauge  of  this  kind  is 
recommended  for  testing  Static  Pressure  Springs  rather  than 
the  use  of  a  portable  dead  weight  tester.  The  pressure  is 
applied  by  filling  the  pump  with  oil  and  forcing  the  oil  into 
the  static  spring  as  well  as  into  the  spring  of  the  test  gauge. 


154 


ORIFICE      METER      MEASUREMENT 


Vacuum  Gauge  Test  Pump 


Fig.  66 


The  pump  shown  here  represents  a  very  efficient  apparatus 
for  testing  vacuum  gauges. 

The  mercury  column  is  graduated  in  inches  and  centi- 
meters. A  small  set  screw  is  provided  on  the  mercury 
reservoir  for  running  out  the  mercury  and  for  accurately  ad- 
justing the  level  of  the  mercury  to  the  zero  point  on  the  scale. 
This  mercury  gauge  requires  about  2j/£  Ib.  of  mercury. 

155 


ORIFICE      METER      MEASUREMENT 


Pocket  Gauge  for  Testing  Differential  Gauges 

This  siphon  or  "U" 
gauge  which  can  be 
conveniently  carried 
about  with  the  mer- 
cury retained  is  adapt- 
ed for  testing  differen- 
tial gauges.  The  scale 
is  graduated  in  inches 
up  to  100  inches  of 
water. 

The  fittings  at  the 
top  joining  the  inlet 
tube  to  the  glass  are 
made  with  two  swivel 
joints,  permitting  the 
glass  and  scale  to  be 
turned  both  laterally 
and  vertically.  When 
the  gauge  is  in  use  the 
glass  is  turned  away 
from  the  inlet  tube, 
thus  opening  the  gas  way  at  the  top,  and  the  outlet  cap  is 
loosened.  When  it  is  to  be  placed  in  the  case,  the  glass  is 
turned  in  toward  the  inlet  tube,  closing  the  gas  way  and  the 
outlet  cap  is  screwed  down,  thus  preventing  the  escape  of 
the  mercury  at  either  side. 

This  apparatus  can  be  used  to  advantage  in  locations 
where  it  is  not  advisable  to  install  a  permanent  gauge  for 
checking  differential  pressures  and  where  the  quantity 
measured  is  comparatively  small.  The  short  length  of  col- 
umns makes  it  impractical  for  use  where  it  is  desired  to  have 
differential  gauge  check  closer  than  one-half  an  inch  of  water 
pressure.  For  accurate  determinations  or  checks  it  is  always 
necessary  to  read  both  columns  of  the  gauge  in  order  to 
obtain  a  correct  differential. 

156 


Fig.   6? 


ORIFICE      METER      MEASUREMENT 


Siphon  or  "U"  Gauges 

For  testing  gauges  whose  maximum  range  is  less  than 
20  inches,  the  type  of  gauge  shown  in  Fig.  68  may  be  used, 
using  water  as  a  fluid. 

These  are  the  most  convenient  low  pressure  gauges  in  use, 
being  portable  and  simply  screwed  to  the  piping  wherever 
it  is  desired  to  take  the  pressure. 

They  consist  of  a  U  shaped  glass  tube  with  a  metal  goose- 
neck, in  sizes  from  4  inch  to  36  inch.  Between  the  columns 
of  this  tube  is  set  a  scale  graduated  in  inches  and  tenths, 
or  pounds  and  ounces,,  as  desired.  A  bent  brass  tube,  or 
goose-neck,  is  connected  to  the  "U"  tube  at  the  top  and  runs 
down  the  side  to  the  gas  connection. 

When  used,  the  gauge  is  filled  with 
water  or  mercury  to  the  center  of  the 
scale,  which  is  zero.  The  gauge  is  con- 
nected to  the  test  tap  and  the  pressure 
is  turned  on.  The  liquid  will  fall 
below  zero  on  the  inlet  side  of  the  "U" 
tube  and  rise  on  the  opposite  side  the 
same  distance.  The  distance  between 
the  two  levels  of  the  liquid,  as  shown 
by  the  scale,  will  indicate  the  amount  of 
pressure  in  inches  and  tenths  or  in  pounds 
and  ounces,  according  to  the  graduation. 
While  the  gauge  is  in  use  the  down- 
ward motion  of  the  liquid  in  one  column, 
due  to  the  pressure  of  the  gas  or  air  should 
equal  the  rise  of  liquid  in  the  opposite  col- 
umn. In  case  the  liquid,  after  being  set  at 
zero,  should  not  drop  on  the  pressure  side  as 
much  as  it  rises  on  the  other  side,  it  is  an 
indication  that  the  glass  tubes  are  not  of 
equal  diameter,  and  both  columns  must  be 
read,  their  sum  being  the  true  pressure. 

157 


Fig.  68— SIPHON  OR 
"U"  GAUGE 


ORIFICE      METER      MEASUREMENT 

Permanent  Gauge  for  Testing  Differential  Gauges 
In  stations  where  there  are  two  or  more  meters  which  are 
being  used  to  measure  very  large  quantities  of  gas  and  where 
it  is  desirable  to  obtain  very  accurate  measurements,  the 
installation  of  a  permanent  test  gauge  is  recommended.  The 
total  range  of  the  test  gauge  being  equal  to  the  maximum 
range  of  the  differential  gauges  in  inches  of  water.  When  using 
a  test  gauge  made  of  two  columns  of  small  bore  glass  tubing, 
the  gauge  should  be  calibrated  between  the  water  levels  in 
the  columns  or  both  columns  of  the  gauge  must  be  read,  as  a 
very  small  difference  in  bore  of  the  tubes  will  make  an  ap- 
preciable difference  in  the  results  if  only  one  column  of  the  U 
tube  is  being  read  and  doubled.  Furthermore,  it  is  quite 
possible  to  obtain  inaccurate  results  due  to  the  water  ad- 
hering to  the  surface  of  the  tube  on  the  high  pressure  side.  A 
reasonable  interval  of  time  should  be  allowed  for  the  water 
to  seek  its  proper  levels  before  reading. 

The  difficulties  of  the  U  tube  consisting  of  two  small  bore 
columns  may  be  obviated  by  using  a  U  tube  in  which  a  high 
pressure  side  is  made  of  a  chamber  of  considerable  area  as 
compared  with  the  low  pressure  column.  That  is,  if  the 
area  of  the  high  pressure  chamber  or  column  is  99  times  as 
great  in  area  as  the  low  pressure  column,  the  water  will  drop 
1  inch  on  the  high  side  while  it  rises  99  inches  in  the  low 
pressure  column  for  a  total  differential  of  100  inches  due  to 
the  fact  that  the  high  pressure  chamber  is  much  greater  in 
area  than  the  low  pressure  column.  The  rise  of  99  inches  in 
the  low  pressure  column  may  be  uniformly  divided  into  100 
parts,  then  each  division  of  y^  of  an  inch  would  represent 
one  inch  of  water  differential.  The  water  in  the  low  pressure 
column  rises  Y/O  °f  an  mcn  while  the  water  in  the  high 
pressure  column  falls  j^j  of  an  inch.  If  the  high  pressure 
column  is  1000  times  the  area  of  the  low  pressure  column  the 
use  of  a  scale  marked  in  inches  would  be  sufficiently  accurate 
as  the  total  error  in  100  inches  would  be  only  y^  of  an  inch 

158 


ORIFICE      METER      MEASUREMENT 

in  water  pressure.  Furthermore,  in  an  installation  of  this 
kind  the  water  adhering  to  the  sides  of  either  column  is  so 
small  when  compared  to  the  total  volume  of  water  that  the 
error  in  levels  would  not  be  appreciable  and  thus  the  neces- 
sity of  waiting  for  the  water  to  seek  its  level  is  eliminated. 
Either  of  the  above  mentioned  gauges  may  be  used  for 
testing  under  pressure,  if  the  fittings  and  material  are  of 
sufficient  strength  to  withstand  the  pressure. 

Portable    Water    Differential    Test    Gauges 

Fig.  69  shows  portable  water  gauges  constructed  on 
the  above  principle  for  testing  gauges  in  the  field  under 
working  conditions. 


Fig.  69 
Courtesy  of  H.  R.  Pierce 


Fig.  70 
Courtesy  of  L.  E.  Ingham 


159 


ORIFICE      METER      MEASUREMENT 

Fig.  70  also  shows  a  small  portable  outfit  which  may  be 
used  for  testing  the  differential  range  of  gauges.  Tube  A 
is  attached  to  the  high  pressure  test  tap.  The  small  cylinder 
made  of  tin  or  copper  is  partly  filled  with  water  as  is 
also  the  rubber  tubing  B  and  the  portion  of  the  glass  tube  C. 
The  glass  tube  C  is  etched  or  marked  and  the  mark  is  held  at 
the  zero  point  of  the  scale  attached  to  the  small  cylinder. 
The  water  is  added  to  the  cylinder  or  through  the  glass  tube 
C  until  its  level  reaches  the  etched  mark.  When  pressure  is 
exerted  on  the  low  pressure  portion  of  the  gauge,  the  same 
pressure  acts  also  on  the  water  in  the  cylinder  causing  water 
to  rise  on  the  glass  tube  C.  For  instance,  if  it  was  desired 
to  test  the  gauge  at  10  inches  differential,  the  glass  tube  C 
is  raised  until  the  etched  mark  is  level  with  the  10  inch  mark 
on  the  scale.  When  pressure  is  exerted  on  the  high  pressure 
side  and  the  differential  pen  arm  rests  at  the  10  inch  mark  on 
the  chart  the  glass  tube  is  moved  either  up  or  down  until  the 
water  surface  reaches  the  etched  mark  and  the  check  reading 
is  obtained  from  the  scale  at  a  point  opposite  the  mark.  It  is 
evident  that  when  the  water  reaches  the  etched  mark  that 
the  surface  of  the  water  in  the  cylinder  is  at  the  same  point 
as  at  the  beginning  of  the  test  or  the  zero  position,  for  the 
combined  volume  of  the  water  in  the  cylinder  below  the 
zero  mark,  in  the  rubber  tube  B,  and  in  the  glass  tube  C  up 
to  the  etched  mark  is  the  same  as  at  the  beginning  of  the 
test.  A  very  small  difference  may  be  caused  by  elasticity 
of  the  rubber  tubing  B  but  since  the  area  of  the  cylinder  is 
very  many  times  as  great  as  the  area  of  the  rubber  tubing 
the  effect  on  the  zero  position  is  negligable.  When  this  ap- 
paratus is  attached  to  the  low  pressure  side  for  testing  under 
a  vacuum  the  connection  is  made  with  the  top  of  the  glass 
tube  C  instead  of  being  made  at  the  top  of  the  cylinder. 


160 


PART  FOUR 

MEASUREMENT  OF  GAS  AND  AIR 


AIR  AND  GAS  MEASUREMENT— COEFFICIENTS 
—MULTIPLIERS  FOR  REVISION  OF  COEFFICIENTS 
-  OSAGE  NATION  SPECIFICATIONS-TABLES  OF  Cv- 
ORIFICE  CAPACITIES— COMPARATIVE  MEASURE- 
MENTS—ATMOSPHERIC PRESSURE  VARIATIONS- 
GAS  CONTRACTS— MULTIPLE  ORIFICE  METER 
INSTALLATION— INSTALLING  AND  TESTING  GAS 
AND  AIR  METERS— READING  CHARTS. 

The  Differential  and  Static  Pressure  Gauge  records 
on  a  chart  the  differential  pressure  existing  between  the 
pressure  connections,  and  the  static  pressure  at  one  of 
the  connections.  These  factors,  with  the  known  area  of 
the  orifice,  enable  the  operator  to  determine  the  flow 
from  the  formula: 

Q  =  C    VAP 

Where  <2  =  the  quantity  of  gas  or  air  passing  the  orifice. 
The  result  is  expressed  in  cubic  feet  per  hour. 

C  =  the  Hourly  Orifice  Coefficient  for  gas  or  air.      The 

value  of  this  term  remains  the  same  for  each  in- 
stallation and  basis  of  measurement. 

h  =  the  Differential  Pressure  existing  between  the  two 
pressure  connections  expressed  in  inches  of 
water  head,  this  value  being  recorded  graph- 
ically on  the  chart  of  the  recording  differen- 
tial gauge. 

161 


MEASUREMENT      OF      GAS      AND      AIR 

P  =  the  Static  Pressure  expressed  in  absolute  units, 
being  equal  to  the  atmospheric  pressure  (which 
is  recorded  on  the  chart)  plus  the  gauge 
pressure.  The  value  of  the  gauge  pressure  is 
also  recorded  on  the  chart. 

The  value  of  the  Hourly  Orifice  Coefficient  C  in  the 
above  formula  is  found  on  Pages  173  to  184,  computed  for 
various  diameters  of  orifice  and  diameters  of  pipe,  these  values 
having  been  determined  by  exhaustive  experimental  and 
practical  tests  in  comparison  with  actual  displacement.  The 
extensions  of  the  values  of  V  hP  have  been  compiled  and 
are  given  in  the  book  entitled  "Pressure  Extensions"  pub- 
lished by  this  Company. 

Example — One  hour  reading  (Air  Flow) : 

Diam.  of  Pipe  =  4  inches.     Diam.  of  Orifice  =  2  inches. 
Average  Differential  reading  h  =  25  inches. 
Base  and  Flowing  Temperature  =  60  degrees  fahr. 
Average  Gauge  Pressure  p  =  90  pounds. 
Hourly  Orifice  Coefficient  C=  1019.4  for  2  inch  orifice  in 
a  4  inch  line  (Page  173). 


Quantity  per  hour,  Q=  1019.4    V  25  X  (90  +  14.4) 

Orifice         Pressure 

=  1019.4X51.088  =  52079  cu.  ft. 

Coefficient.      Extension. 

Using  the  same  data,  when  measuring  gas  at  a  4  oz. 
Pressure  Base,  the  Hourly  Orifice  Coefficient  C  is  1293.7  for 
a  2  inch  orifice  in  a  4  inch  line,  (Table  29,  Page  175), 

Orifice       Pressure 

(2=1293.7  V25X (90+14.4)  =  1293.7X51.088 

Coefficient.      Extension. 

or  the   volume   passing   through   the   orifice  =  66093   cubic 
feet  per  hour. 

Therefore  the  Quantity  per  hour  flowing  in  the  lines  is 
equal  to  the  Coefficient  of  the  Disc  multiplied  by  the  Pres- 
sure Extension. 

162 


MEASUREMENT      OF      GAS      AND      AIR 

In  the  formula  V  =  Cv-^2gH  the  differential  head  or  the 
difference  in  pressure  between  the  upstream  side  of  the  ori- 
fice and  the  downstream  side  of  the  orifice  is  expressed  in 
feet  head  of  flowing  fluid  and  as  it  is  not  practical  to  register 
this  value  directly,  the  differential  head  is  recorded  on  the 
chart  in  inches  of  water. 

Using  the  same  data  as  used  on  Page  80  in  determination 
of  the  value  of  the  air  coefficient,  the  details  of  the  develop- 
ment of  the  values  of  the  constants  for  the  formula  for  the 
flow  of  air  and  gases  are  given  below. 

1  foot  head  of  air  at  32  deg.  fahr.  (492  degrees  absolute) 
at  14.7  Ib.  per  sq.  in.  =  .015534  inches  of  water. 

Therefore,  1  inch  of  water -64.375  feet  of  air  at  32  de- 
grees at  14.7  Ib.  (1^.015534  =  64.375). 

Since  the  volume  increases  as  the  pressure  decreases, 
1  inch  of  water  =  946.31  feet  of  air  at  32  degrees  at  1  Ib. 
per  sq.  in.  absolute.  (64.375X14.7  =  946.31). 

Referring  to  Part  2,  we  find  that  the  volume  decreases  as 
the  temperature  decreases. 

1  inch  of  water  =  1.9234  feet  of  air  at  1  deg.  fahr.  absolute 
at  1  Ib.  per  sq.  in.  absolute.  (946.31^492  =  1.9234). 

For  any  pressure  and  temperature : 

1  inch  of  water  =  —  -  feet  of  air  at  T  degrees  ab- 

solute at  P  Ib.  absolute,  according  to  the  Law  of  Perfect 
Gases. 

Where    T  =  Temperature  in  deg.  fahr.  absolute. 

P  =  Pressure  in  pounds  per  square  inch  absolute. 

For  gas,  as  the  Specific  Gravity  G  increases  the  weight  per 
cubic  foot  increases,  and  the  differential  head  in  feet  head  of 
gas  decreases,  and  vice  versa. 

1.9234Z\  , 

1  inch  of  water  =  -         — feet  head  of  gas. 
PG 

163 


MEASUREMENT      OF      GAS      AND      AIR 


MEASUREMENT      OF      GAS      AND      AIR 


1  9234  Th 

Then  h  inches  of  water  =  — feet  head  of  gas, 

PG 

But  H  feet  of  gas  equals  h  inches  of  water, 

1  9234  hT 

Therefore,  H  =  —  -  in  feet  head  of  gas, 

PG 

Where  H  =  differential  pressure  expressed  in  feet  head 

of  flowing  gas. 
h  =  differential  in  inches  of  water. 

Substituting  this  value  of  H  in  the  formula 
r,  we  obtain 


;          v=c       |2gX1.9234^1113          Iff 
\  PG  VPG 

Where  V  =  actual  velocity  of  gas  passing  the  orifice,  at 

temperature  T  and  pressure  P. 
Cv  =  coefficient  of  velocity. 

g  =  acceleration  due  to  gravity  in  feet  per  second, 

per  second,  (32.2  used  on  Page  80). 
1  .  9234  =  feet  head  of  air  at  1  deg.  fahr.  absolute  at  1  Ib. 
per  sq.  in.  absolute  equivalent  to  one  inch  of  water. 
h  =  differential  in  inches  of  water. 
T  =  temperature  in  deg.  fahr.  absolute. 
p=  pressure  in  pounds  per  sq.  in.  absolute. 
G  =  specific  gravity  of  gas  (air  =  l) 

The  quantity  of  gas  passing  through  the  orifice  is  equal 
to  the  area  of  the  orifice  in  square  feet  multiplied  by  the 
velocity  in  feet  per  hour 


144 

X  V 
165 


MEASUREMENT      OF      GAS      AND      AIR 

Where  Q\  =  actual  quantity  of  gas  passing  the  orifice  in 
cubic  feet  per  hour,  at  the  pressure  and  tem- 
perature of  the  flowing  gas. 

0.7854<Z2 

—  =area  01  orifice  in  sq.  ft. 
144 

d  =  diameter  of  orifice  in  inches. 
144  =  number  of  sq.  in.  in  a  sq.  ft. 
3600  =  seconds  in  one  hour. 

V  =  velocity  of  gas  through  orifice  in  feet  per  sec. 

Substituting  the  value  of  V  where 

]\hf 
V=ll.l3Cv  V'TY->   m   tne   formula   from    the 

preceding  page,  Q1  =  19Md2XV. 
X  11.13  C 


d  =  218.6 

Since  the  gas  is  measured  under  standard  conditions  of 
Base  Temperature  and  Pressure  Base  it  is  really  measured 
by  weight  by  the  introduction  of  these  terms. 

From  the  Law  of  Perfect  Gases,  Page  59,  (in  this  case  Q 
is  substituted  for  v) 


Tb        T 

Where  Pb  =  Pressure    Base   in   pounds    per    square    inch 

absolute. 
P  =  actual  pressure  of  flowing  gas  in  pounds  per 

square  inch  absolute. 
Q  =  volume  of  gas  passing  orifice  expressed  in  cubic 

feet  at  a  Pressure  Base  Pb  and  a  Base  Tem- 

perature TV 

166 


MEASUREMENT      OF      GAS      AND      AIR 


Fig.  72— 50  INCH  DIFFERENTIAL  GAUGE,  FLANGE   CONNECTIONS 


167 


MEASUREMENT       OF      GAS      AND      AIR 

Qi  =  volume  in  cubic  feet  passing  the  orifice  at 
actual  Flowing  Temperature  and  Pressure  of 
the  gas  or  air. 

rfc  =  Base  Temperature  in  deg.  fahr.  absolute. 

T  =  Flowing  Temperature  in  deg.  fahr.  absolute. 


Then    Q  =  QiX- 

PbT 

Substituting  the  value  of  Qi  from  the  previous  formula 
Qi  =  218.6  Cvd2  \j^7^  in  this  expression. 


Q=  218.6  Cvd 

*  PG     Pb' 

>Th    \h  P 


In  this  formula  218.6  is  a  constant  depending  on  the 
units  of  measurements.  On  Page  81  the  constant  for  a 
fifteen  minute  period  is  54.65  being  one  fourth  of  218.6  the 
constant  for  one  hour. 

The  net  result  of  these  factors  is  expressed  in  the  formula : 


TG 

Where  Q  =  Quantity  of  gas  passing  the  orifice  expressed  in 
cubic  feet  at  a  Base  Temperature  and  a  Pressure 
Base. 

K  =  Constant  dependent  upon  the  value  of  g,  weight 
of  water  per  cubic  foot  and  units  of  measure- 
ment. 

Cv  =  Coefficient  of  Velocity.  The  value  of  this  term 
depends  upon  the  location  of  the  pressure 
connections  in  the  main  line,  diameter  of  ori- 
fice, internal  diameter  of  pipe  and  ratio  of 
differential  to  line  pressure. 

168 


MEASUREMENT      OF      GAS      AND      AIR 

d  =  diameter  of  orifice  in  inches. 

r6  =  Base  Temperature  in   deg.  fahr.  absolute  =  460+ 
Base  Temperature   in   degrees   fahrenheit  on 
an  ordinary  thermometer  scale. 
Pb  =  Pressure  Base  in  pounds  per  square  inch  absolute. 

P  =  pressure  of  flowing  gas  in  pounds  per  square  inch 
absolute  =  atmospheric  pressure  +  gauge  pres- 
sure p.  When  gas  is  measured  under  a  vacuum, 
P  =  atmospheric  pressure  (in  pounds  per  square 
inch)  —  0.4908  X  (inches  of  mercury  vacuum). 

h  =  Differential  Pressure  between  the  connections 
expressed  in  inches  of  water. 

T  =  temperature  of  flowing  gas  in  deg.  fahr.  absolute 
=  460+  temperature  in  degrees  fahrenheit. 

G  =  Specific  Gravity  of  gas  compared  with  air,  which 
is  1. 

The  Hourly  Coefficient  C  in  Tables  27  to  38 

=  218.6  Cvd2     Tb_ 
Pb^TG 

Thus  it  is  seen  that  the  Coefficient  is  dependent  upon  the 
values  used  for  K,  CV)  d,  Pb,  Tb,  T  and  G. 

Where  the  conditions  of  flow  are  defined,  this  formula  is 
simplified  as  follows:—  (Table  27,  Page  173). 

Tb  =  60  deg.  fahr.  =  520  degrees  absolute. 

P6  =  01b.   above  atmosphere   (14.4  Ib.)  =14.4  Ib. 

per  sq.  in.  absolute. 
r  =  60  deg.  fahr.  =  520  deg.  absolute. 
G  =  1.00 


c_  218.6  ^n_21S6      520  C/ 


C  =  346.2  Cvd2. 


169 


MEASUREMENT      OF      GAS      AND      AIR 


Fig     73— ORIFICE,   FLANGES   AND    100   INCH    DIFFERENTIAL   GAUGE 

INSTALLATION.     PIPE   TAP  CONNECTIONS.     NOTE  BY-PASS 

BETWEEN  GAUGE  LINES 


170 


MEASUREMENT      OF      GAS      AND      AIR 

The  Coefficients  in  Tables  27  to  38  are  prepared  for  pipe 
of  standard  dimensions  (4.026,  6.065,  8.071  and  10.191  inches 
internal  diameter),  for  installations  where  the  pressure  con- 
nections are  made  2J/2  diameters  upstream  and  8  diameters 
downstream.  These  Hourly  Orifice  Coefficients  were  based 
on  the  original  Hourly  Orifice  Coefficients  (changed  for  pres- 
sure base  only).  They  were  calculated  from  the  various 
values  of  Cv  obtained  by  inspection  from  a  smooth  curve, 
drawn  as  a  mean  through  the  values  of  Cv  obtained  by  tests 
as  described  in  Part  3.  The  values  of  Cv  were  obtained  by 
using  the  constants  used  in  this  article,  which  constants 
should  be  used  for  calculating  orifice  coefficients  where  the 
conditions  do  not  vary  materially  from  the  conditions  of  the 
tests. 

The  values  of  Cv  contained  on  Pages  208  to  210  were  cal- 
culated from  a  formula*  which  was  derived  several  years 
later  from  four  points  on  a  curve  drawn  in  a  similar  manner 
to  the  above.  These  values  do  not  vary  more  on  an  average 
than  grQ-  of  one  percent  from  the  values  of  Cv  previously 
mentioned,  some  of  the  values  being  slightly  lower  and 
some  higher,  than  those  used  in  the  original  calculations. 

The  published  values  of  the  air  and  gas  Coefficients  are 
retained  in  this  volume  in  their  original  form.  Their  reli- 
ability is  not  increased  by  any  change  except  by  a  series  of 
tests  much  more  comprehensive  than  those  previously  con- 
ducted. Future  tests  will  no  doubt  take  into  consideration 
the  humidity  of  the  atmosphere,  and  the  slight  variations 
due  to  pressures,  differentials,  specific  gravity,  viscosity  of 
the  fluid,  etc.  When  such  tests  are  made,  it  is  hoped  that 
they  shall  be  conducted  by  an  authority  superior  to  the 
operator  and  the  manufacturer  and  that  their  findings  may 
be  binding  upon  both  the  buyer  and  the  seller,  such  as 
standard  weights  and  measures  are  today. 

*By  H.    R.    Pierce. 

171 


MEASUREMENT      OF      GAS      AND      AIR 

In  calculating  Hourly  Orifice  Coefficients  for  all  other 
dimensions  of  pipe  not  contained  in  the  original  tables,  the 
use  of  the  values  of  Cv  from  Pages  208  to  210  is  recom- 
mended due  to  the  fact  that  any  two  parties  will  be  sure  to 
use  the  same  value,  and  ,thus  avoid  any  controversy  which 
may  arise  over  a  value  obtained  by  inspection  from  a  plotted 
curve. 

Coefficients  for  pipes  of  other  internal  diameters  may  be 
obtained  by  substituting  in  the  previous  formula  the  proper 
values  for  the  pressures,  temperatures,  etc.,  using  the  value 
of  218.6  for  K. 

Example  —  Coefficient  for  a  !}/£  inch  orifice  in  a  pipe 
5.188  inches  in  diameter  is  desired.  •  Pressure  Base  8  oz. 
above  an  atmospheric  pressure  of  14.4  Ib.  per  square  inch. 
Base  and  Flowing  Temperature  60  deg.  fahr.  Specific 
Gravity  1.00. 

Pb  -  14.4+0.5  =  14.9  Ib.  per  sq.  in.  absolute. 

Tb  =  60+460  -520  deg.  fahr.  absolute. 

G  -1.00 

X  —diameter  of  orifice  -4-  diameter  of  pipe  =.2891. 

C,=  .6414,  Page  208. 

C  =  218.6  Cvd 

218.6X.6414X1.5X1.5X520 


14.9V520X1 


Fig.  74— PIPE.  SADDLE 
172 


MEASUREMENT      OF      GAS      AND      AIR 


Table  27— HOURLY  ORIFICE  COEFFICIENTS 
FOR  GAS  AND  AIR 

Pressures  taken  2^  diameters  upstream  and  8  diameters  downstream. 
Atmospheric  Pressure  14.4  Ib.      Base  and  Flowing  Temperature  60  deg.  fahr. 

Pressure  Base  0  lb._(14.4  Ib.  Abs.)         Specific  Gravity  1.00 

Values  of  C  in  Q  =  C  VhP  where  Q  =  quantity  of  gas   or  air  passing  the  orifice 
in  cubic  feet  per  hour. 


DIAMETER 
OP 


DIAMETER  OF  PIPE  LINE 


ORIFICE 
INCHES 

4" 

6" 

8" 

10" 

y* 

53.20 

52.88 

52.72 

52.67 

% 

83.55 

% 

121.1 

119.6 

119.1 

118.8 

1/8 

166.2 

1 

219.2 

214.3 

212.7 

212.0 

l/^ 

280.4 

1M 
1% 

350.6 
430.1 

338.3 

'334.'2 

332.5 

519.9 

493.2 

484.6 

480.6 

j5/ 

621.8 

1/4 

738.2 

681.0 

665.0 

657.5 

jT/ 

870.2 

2 

1019.4 

904.1 

876.4 

863.8 

gi/g 

1189.3 

2/4 

1382.5 

1169.1 

1121.8 

1100.9 

g3^ 

1610.8 

23/2 

1856.2 

1480.4 

1401.2 

1368.8 

2% 

2146.8 

**Xo 

2M 

2481.9 

1851.2 

1718.5 

1670.0 

2^ 

2860.2 

3 

3296.2 

2287.2 

2078.8 

2004*9 

3J4 

2806.9 

2485.1 

2371.9 

31^ 

3428.1 

2950.5 

2788.3 

3?4 

4166.8 

3474.7 

3243.3 

4 

5050.4 

4070.0 

3742.9 

4/4 

6103.8 

4752.4 

4296.0 

41^ 

7358.2 

5519.5 

4909.0 

4/4 

6411.7 

5583.7 

5 

7407.7 

6330.8 

8575.8 

7164.0 

&A 

9906.9 

8071.2 

5/4 

11406.5 

9098.9 

6 

13131.1 

10225.4 

6/4 

11481.2 

6^ 

12885.9 

6^4 

14448.0 

7 

16196.3 

734 

18125.0 

73^ 

20249.0 

173 


MEASUREMENT      OF      GAS      AND      AIR 


Table  28— HOURLY  ORIFICE  COEFFICIENTS  FOR  GAS 

Pressures  taken  2^£  diameters  upstream  and  8  diameters  downstream. 
Atmospheric  Pressure  14 .4  Ib  .        Base  and  Flowing  Temperature  60  deg .  f ahr . 

Pressure  Base  0  Ib.  (14.4  Ib.  Abs.).          Specific  Gravity  .600 

Values  of  C  in  Q  =  C  VhP  where  Q=  quantity  of   gas  passing  the   orifice  in 
cubic  feet  per  hour. 


DIAMETER 
OF 


DIAMETER  OF  PIPE  LINE 


URIFICE 

INCHES 

4" 

6" 

8" 

10  ;/ 

H 

68.68 

68.27 

68.06 

68.00 

% 

107.90 

% 

156.3 

154.4 

153.8 

'l53.4 

% 

214.6 

282.9 

'276.'7 

274.6 

'273.'7 

m 

362.0 

m 

452.6 

'486.8 

431.5 

429.2 

IH 

555.3 



m 

671.2 

636^7 

625.6 

620^5 

i*A 

802.8 

IK 

953.0 

879.1 

858.5 

848.8 

VA 

1123.4 

2 

1316.1 

1167.2 

1131.4 

1115.'2 

2ys 

1535.4 

2H 

1784.8 

1509^3 

1448.2 

1421  .'2 

2*/s 

2079.5 

2y2 

2396.3 

1911.  '2 

1808  .'9 

1767.2 

25/8 

2771.5 

2% 

3204.1 

2390^0 

2218.'  6 

2155.9 

27A 

3692.5 

u/& 

3 

4255.3 

2952.7 

2683.8 

2588.3 

3U 

3623.7 

3208.3 

3062.2 

u/4 

3^ 

4425.6 

3809.1 

3599.7 

3% 

5379.3 

4485.8 

4187.1 

*-'/4 

4 

6520.0 

5254.4 

4832.0 

4M 

7880.0 

6135.3 

5546.1 

4M 

9499.4 

7125.7 

6337.3 

4^ 

8277.5 

7208.5 

5 

9563.3 

8173.0 

5k' 

11071.3 

9248.6 

5l/2 

12789.7 

10419.8 

&A 

14725.7 

11746.6 

6 

16952.1 

13200.9 

Q1A 

14822.1 

v/4. 

&A 

16634.3 

&/A 

18652.1 

v/4 

7 

20909.1 

7U 

23399  .  2 

1  /  4r 

7^2 

26141.3 

1  /  £4 

174 


MEASUREMENT      OF      GAS      AND      AIR 


Table  29— HOURLY  ORIFICE  COEFFICIENTS  FOR  GAS 

Pressures  taken  2^  diameters  upstream  and  8  diameters  downstream. 
Atmospheric  Pressure  14.4  Ib.  Base  and  Flowing  Temp.  60  deg.  fahr. 

Pressure  Base  4  oz.J14.65  Ib.  Abs.)  Specific  Gravity  .600 

Values  of  C  in  Q  =C  VhP  where  Q  =  quantity  of  gas  passing  the  orifice   in  cubic 
feet  per  hour. 


DIAMETER 

OF 


DIAMETER  OF  PIPE  LINE 


ORIFICE 

INCHES 

4" 

Q" 

8" 

10" 

1A 

67.5 

67.1 

66.9 

66.8 

5A 

106.0 

H 

153.7 

151.8 

151.2 

150.8 

210.9 

i 

278.1 

272.0 

269.8 

269.1 

ji/g 

355.8 

11^ 

444.9 

429.4 

424.1 

421.9 

liHj 

545.9 

i/^ 

659.8 

'625  .'9 

615.0 

609.9 

1^8 

789.1 

1/4 

936.8 

864.2 

844.0 

834.4 

l/^ 

1104.3 

2 

1293.7 

1147.4 

1112.2 

1096.2 

2//s 

1509.3 

234 

1754.5 

1483  .'7 

1423.'  6 

1397.0 

2^8 

2044.1 

K//  o 

2355.6 

1878.7 

1778  .'2 

1737.1 

2^8 

2724.4 

2% 

3149.7 

2349.4 

2180.'  8 

2119.'3 

g.TX 

3629  8 

3 

4183.0 

2902.5 

2638.2 

2544.3 

3M 

3562.2 

3153.7 

3010.1 

31^ 

4350.4 

3744.4 

3538.5 

3% 

5287.9 

4409.6 

4116.0 

4 

6409.2 

5165.0 

4749.9 

4/€ 

7746.1 

6031.0 

5451.8 

4/^ 

9337.9 

7004.5 

6229.6 

4^ 

8136.8 

7084.7 

5 

9400.8 

8034.1 

5/4 

10883.2 

9091.4 

51^ 

12572.3 

10242.7 

5/€ 

14475.4 

11547.0 

6 

.... 

16664.0 

12976.5 

gi/ 

14570.1 

6^ 

16350.0 

6^ 

18335.1 

u/4 

7 

20553.8 

23001  .  5 

7i/ 

25697.0 

175 


MEASUREMENT      OF      GAS      AND      AIR 


Table  30— HOURLY  ORIFICE  COEFFICIENTS  FOR  GAS 

Pressures  taken  2^  diameters  upstream  and  8  diameters  downstream. 
Atmospheric  Pressure  14.4  Ib.  Base  and  Flowing  Temp.  60  deg.  fahr. 

Pressure  Base  8  oz._(14.9  Ib.  Abs.)          Specific  Gravity  .600 

Values  of  C  in  Q  =C    VhP    where  Q  =  quantity  of   gas    passing   the    orifice    in 
cubic  feet  per  hour. 


DIAMETER 

OF 


DIAMETER  OF  PIPE  LINE 


ORIFICE 
INCHES 

4" 

6" 

8" 

10" 

K 
*A 

66.4 
104  2 

66.0 

65.8 

65.7 

H 

j2 

151.1 
207  4 

149.3 

148.3 

148.2 

\y% 

273.4 
349  8 

267.4 

265.3 

,     264.5 

V4 
IH 

437.4 
536  7 

422.1 

417.0 

414.8 

iy2 

l*A 
l*A 

1% 

648.7 
775.8 
921.0 
1085.7 

615.3 
849.6 

604.6 
829.7 

599.7 
820.3 

2 

2% 

1271.9 
1483  9 

1128.0 

1093.4 

1077.7 

2% 
2% 

1724.9 
2009  7 

1458.7 

1399.6 

1373.5 

2y2 
2% 
2% 
2% 
3 
3X 

sy2 

&A 

4 

4M 
4j| 

2315.9 
2678.5 
3096.6 
3568.6 
4112.5 

1847.  1 
2309.8 

2853.6 
3502.1 
4277.  1 
5198.8 
6301.2 
7615.6 
9180  6 

1748.2 
2144.1 

2593.7 
3100.6 
3681.3 
4335.3 
5078.0 
5929.4 
6886  5 

1707.9 
2083.5 

2501.4 
2959.4  ' 
3478.9 
4046.6 
4669.9 
5360.0 
6124  7 

4% 
5 

5M 

5l/2 

&A 

6 

Q1A 

7999.7 
9242.4 
10699.8 
12360.5 
14231.5 
16383.3 

6966.6 
7898.7 
8938.3 
10070.2 
11352.4 
12757.9 
14324  7 

VA 

&A 

7 

VA 

V/2 

16076.1 
18026.2 
20207.5 
22613.9 
25264.0 

176 


MEASUREMENT      OF      GAS      AND      AIR 


Table  31— HOURLY  ORIFICE  COEFFICIENTS  FOR  GAS 

Pressures  taken  2J^  diameters  upstream  and  8  diameters  downstream. 
Atmospheric  Pressure  14.4  Ib.  Base  and  Flowing  Temp.  60  deg.  fahr. 

Pressure  Base  10  oz.  (15.025  Ib.  Abs.)       Specific  Gravity  .600 

Values  of  C  in  Q  =C  VhP  where  Q  =quantity  of  gas  passing  the  orifice  in  cubic 
feet  per  hour 


DIAMETER 

OF 


DIAMETER  OF  PIPE  LINE 


ORIFICE 
INCHES 

4" 

6" 

8" 

10" 

1 

65.8 
103  4 

65.4 

65.2 

65.2 

H 

7A 

149.8 
205  7 

148.0 

147.4 

147.0 

\YC, 

271.2 
346  9 

265.2 

263.0 

262.3 

VA 
i3A 

433.7 
532  2 

418.6 

413.5 

411.4 

11A 

m 

1% 

$ 

2y8 

2*A 

2% 

643.3 
769.4 
913.3 
1076.6 
1261.3 
1471.6 
1710.6 
1993  0 

610.2 
842.5 

ins.'e 

1446.5 

599.6 
822*8 
1084.3 
1388.0 

594.7 
813.5 
1068.7 
1362.1 

2y2 

25A 
2% 
27A 

2296.6 
2656.2 
3070.9 
3538.9 

1831.7 
2290.6 

1733.7 
2126.3 

1693.7 
2066.2 

3 

3M 
31A 
3H 

4M 
4^ 
4% 
5 
5^ 

4078.3 

2829.9 
3473.0 
4241.5 
5155.5 
6248.8 
7552.2 
9104.2 

2572.1 
3074.8 
3650.7 
4299.2 
5035.8 
5880.1 
6829.2 
7933.2 
9165.5 
10610.8 

2480.6 
2934.8 
3450.0 
4013.0 
4631.0 
5315.4 
6073.7 
6908.6 
7833.0 
8863.9 

5U 

12257  7 

9986.4 

&A 

14113  1 

11258.0 

6 

Q1A 

16247.0 

12651.8 
14205.5 

Q1A 
&A 



15942.4 
17876.2 

7 

20039.4 

7M 

22425.8 

7^ 

25053.9 

177 


MEASUREMENT      OF      GAS      AND      AIR 


Table  32— HOURLY  ORIFICE  COEFFICIENTS  FOR  GAS 

Pressures  taken  2l/%  diameters  upstream  and  8  diameters  downstream. 
Atmospheric  Pressure  14.4  Ib.  Base  and  Flowing  Temp  60  deg.  fahr. 

Pressure  Base  1  lb^(15.4  Ib.  Abs.)         Specific  Gravity  .600 

Values  of  C  in  Q  =C  VhP    where    Q  =    quantity  of    gas  passing  the    orifice  in 
cubic  feet  per  hour. 


DIAMETER 
OF 


DIAMETER  OF  PIPE  LINE 


ORIFICE 
INCHES 

4" 

Q" 

8" 

10" 

1A 
5A 
% 

% 

iy* 

64.2 
100.9 
146.2 
200.6 
264.6 
338.5 

63.8 
144.4 
258.7 

63.6 
143.8 
256.8 

63.6 
143.4 
256.0 

8 

423.2 
519  3 

408.4 

403.4 

401.4 

8 

\*A 

627.7 
750  6 

595.4 

585.0 

580.2 

1% 

iy8 

2 

2% 
&A 
2% 

891.1 
1050.4 
1230.6 
1435.7 
1668.9 
1944  5 

822.0 
1091.4 
1411.3 

802.8 
1057.9 
1354.2 

793.7 
1042.7 
1328.9 

21A 

2% 

2240.7 
2591  6 

1787.1 

1691.4 

1652.4 

&A 

2% 
3 
3^ 

3y2 

&A 
4 

4^ 

43^ 

4% 

2996.1 
3452.8 
3979.0 

2234.8 

2761.0 
3388.4 
4138.2 
5030.0 
6096.6 
7368.3 
8882.5 

2074.5 

2509.5 
2999.9 
3561.8 
4194.5 
4913.2 
5736.9 
6662.9 
7740.0 

2015.9 

2420.2 
2863.3 
3366.0 
3915.2 
4518.3 
5185.9 
5925.8 
6740.4 

5 

5^ 
5^ 
5% 
6 

8942.3 
10352.4 
11959.2 
13769.6 
15851  3 

7642.3 
8648.1 
9743.2 
10983.8 
12343.7 

Ql/i 

13859.6 

&A 
6% 
7 
7H 
71A 

15554.2 
17440.9 
19551.4 
21879.7 
24443.8 

178 


MEASUREMENT      OF      GAS      AND      AIR 


Table  33— HOURLY  ORIFICE  COEFFICIENTS  FOR  GAS 

Pressures  taken  2*^  diameters  upstream  and  8  diameters  downstream. 
Atmospheric  "Pressure  14 .4  Ib .        Base  and  Flowing  Temperature  60  deg .  fahr . 

Pressure  Base  1^  lb^(15.9  Ib.  Abs.).        Specific  Gravity  .600 

Values  of  C  in  0   =  C  VhP  where  Q   =  quantity  of  gas  passing  the  orifice  in 
cubic  feet  per  hour. 


DIAMETER 
OF 


DIAMETER  OF  PIPE  LINE 


(JRIFICE 

INCHES 

4" 

6" 

8" 

10" 

X 
to 

x 

Vv 

62.2 
97.7 
141.6 
194  3 

61.8 
'l39.9 

61.6 
139.3 

61.6 
138^9 

I 

iys 
ix 

13/C 

256.2 
327.8 
409.9 
502  9 

250.6 
395.6 

248.7 
390^8 

247.9 
388.7 

IK 

1% 

1M 

1% 

2 

2ys 

21A 

2% 

607.9 
727.0 
863.1 
1017.4 
1191.9 
1390.6 
1616.4 
1883  3 

576'.  6 
'796^2 
1057.1 
1366.9 

566.6 

777.6 
1024^7 
1311.6 

562.0 
768.7 
1009^9 
1287  .'l 

2y2 

25/8 

&A 

27A 

2170.3 
2510.1 
2901.9 
3344  2 

1730.9 
2164^5 

1638.2 
2009^3 

1600.5 
1952^5 

3 
3M 
3\4 

3853.9 

2674.4 
3281.9 
4008.1 

2430.6 
2905.6 
3449.8 

2344.1 
2773.3 
3260.1 

3M 

4 

4J4 
4^ 
4M 

4871.8 
5904.9 
7136.6 
8603.2 

4062.6 
4758.7 
5556.5 
6453.4 
7496.6 

3792.1 
4376.2 
5022.9 
5739.5 
6528  4 

5 

8661.1 

7402.0 

5K 

10026.9 

8376  .  1 

51A 
53/X 
6 

11583.1 
13336.5 
15352.9 

9436.8 
10638.4 
11955.5 

61A 

13423.8 

sy2 

15065.0 

6M 

16892.5 

7 

18936.6 

7K 

21191.7 

7K 

23675.2 

179 


MEASUREMENT      OF      GAS      AND      AIR 


Table  34— HOURLY  ORIFICE  COEFFICIENTS  FOR  GAS 

Pressures  taken]23^  diameters  upstream  and  8  diameters  downstream. 
Atmospheric  Pressure  14 .4  Ib .        Base  and  Flowing  Temperature  60  deg.  fahr . 

Pressure  Base  2  Ib.  (16.4  Ib.  Abs.).          Specific  Gravity  .600 

Values  of  C  in  Q  =  C    VhP  where   Q   =   quantity  of  gas  passing  the  orifice  in 
cubic  feet  per  hour. 


DIAMETER 

OF 

DIAMETER  c 

>F  PIPE  LINE 

INCHES 

4" 

6" 

8" 

10" 

K 

% 
% 

% 

60.3 
94.7 
137.3 

188.4 

59.9 
135.6 

59.8 
135.  i 

59.7 
134.7 

lYs 

248.4 
317  8 

243.0 

241.1 

240.3 

IX 

1*2 

397.4 
487  6 

383.5 

378.8 

376.9 

ilA 

1% 

589.4 
704.9 

559.1 

549.3 

544.8 

IK 
1J4 

836.7 
986  4 

771.9 

753.8 

745.3 

2 

2V* 

1155.6 
1348  2 

1024.9 

993.4 

979.1 

*1A 

2¥8 

21A 
2&i 

1567.1 
1825.9 
2104.1 
2433  5 

1325.3 

1678.1 

1271.6 
1588  .'3 

1247.9 
1551.7 

2H 

2H 
3 

&A 

VA 

3% 
4 

4^ 
4^ 
4M 
5 
5^ 

2813.4 
3242.2 
3736.4 

2098.5 

2592.6 
3181.8 
3885.9 
4723.3 
5724.9 
6919.0 
8340.9 

1948.0 

2356.5 
2817.0 
3344.6 
3938.8 
4613.6 
5387.1 
6256.7 
7268.0 
8397.1 
9721.2 

1893.0 

2272.6 
2688.7 
3160.7 
3676.5 
4242.8 
4869.7 
5564.5 
6329.4 
7176.3 
8120.7 

&A 

11229.9 

9149.1 

5% 

12929.9 

10314.1 

6 

6M 

14884.8 

11591.0 
13014.5 

VA 

6M 
7 
7^ 

VA 

14605.7 
16377.5 
18359.3 
20545.6 
22953.3 

180 


MEASUREMENT      OF      GAS      AND      AIR 


Table   35— HOURLY  ORIFICE   COEFFICIENTS  FOR 
GAS  AND  AIR 

Pressures  taken  2J^  diameters  upstream  and  8  diameters  downstream. 
Atmospheric  Pressure  14.7  Ib.        Base  and  Flowing  Temperature  60  deg.  fahr. 

Pressure  Base  0  oz.  (14.7  Ib.  Abs.).        Specific  Gravity  1.00 

Values  of  C  in  Q  =C  VhP  where  Q  =  quantity  of  gas  or  air  passing  the 
orifice  in  cubic  feet  per  hour. 


DIAMETER 

OF 

DIAMETER  o 

F  PIPE  LINE 

ORIFICE 
INCHES 

4" 

6" 

8" 

10" 

y* 

52.11 

51.80 

51.64 

51.60 

b/s 

81.84 

H 

118.6 

117.2 

116^7 

116.4 

7A 

162.8 

214.7 

209^9 

208^4 

207^7 

IX 

274.7 

IK 

343.4 

331.4 

327^4 

32$.  7 

IX 

42-1.3 

ilA 

509.3 

483.1 

'474.7 

470^8 

15A 

609.1 

1% 

723.1 

667.1 

651.4 

644.1 

IX 

852.4 

2 

998.6 

885.6 

858.5 

846.2 

2Y8 

1165.0 

21A 

1354.3 

1145.2 

1098.9 

1078.4 

2% 

1577.9 

&A 

1818.3 

1450.2 

1372.6 

1340.9 

2H 

2103.0 

2% 

2431.2 

1813.4 

1683.4 

1635^9 

27/8 

2801.8 

3 

3228.9 

2840  .'5 

2036.4 

1964  'O 

3M 

2749.6 

2434.4 

2323.5 

m 

3358.1 

2890.3 

2731.4 

3M 

4081.8 

3403.8 

3177.1 

4 

4947.3 

3986.9 

3666.5 

4M 

5979.2 

4655.4 

4208.3 

4^ 

7208.0 

5406.9 

4808.8 

4^ 

6280.9 

5469.7 

5 

7256.5 

6201  .  6 

fyi 

8400.8 

7017.8 

&A, 

9704  .  7 

7906.5 

5% 

11173.7 

8913.2 

6 

12863.1 

10016.7 

§y± 

11246.9 

V/2 

1262,2.9 

&A 

14153.1 

7 

15865.8 

VA 

17755.1 

7^ 

19835.8 

181 


MEASUREMENT      OF      GAS      AND      AIR 


Table  36— HOURLY  ORIFICE  COEFFICIENTS  FOR  GAS 

Pressures  taken  2>£  diameters  upstream  and  8  diameters  downstream. 
Atmospheric  Pressure  14.7  Ib.        Base  and  Flowing  Temperature  60  deg.  fahr. 

Pressure  Base  4  oz.  (14.95  Ib.  Abs.).        Specific  Gravity  .60 
Values  ofCinQ  =C   Vhp  where   Q   =  quantity  of  gas  passing  the  orifice 
in  cubic  feet  per  hour. 


DIAMETER 

OF 

DIAMETER  o 

F  PIPE  LINE 

ORIFICE 
INCHES 

4" 

6" 

8" 

10" 

V* 

66.15 

65.76 

65.56 

65.50 

% 

103.9 

% 

150.6 

148.7 

148.1 

147.7 

1/K 

206.7 

1 

272.6 

266^5 

264^5 

263.6 

\\/n 

348.7 

1/4 

436.0 

420.7 

415.6 

413.5 

l/^ 

534.8 

\y2 

646.5 

613.3 

602.6 

597.6 

l/^ 

773.2 

\y± 

918.0 

846.8 

'826.9 

817.6 

\T/Q 

1082.1 

2 

1267.6 

1124.2 

1089.8 

1074.1 

2^8 

1478.9 

2% 

1719.1 

1453.'  8 

1395.0 

1369.0 

2% 

2003.0 

21A 

2308.2 

1840^9 

1742.4 

1702.1 

2669.5 

2% 

3086.2 

2302^0 

2137.0 

2076^6 

27/8 

3556.7 

3 

4098".  8 

2844.1 

2585.0 

2493.1 

3/4 

3490.4 

3090.2 

2949.5 

31^2 

4262.8 

3668.9 

3467.3 

3% 

5181.4 

4320.8 

4033.0 

4 

6280.2 

5061.0 

4654.3 

4/4 

7590.1 

5909.6 

5342.1 

43^ 

9149.9 

6863.5 

6104.3 

4/4 

7972.9 

6943.3 

5 

9211.5 

7872.3 



10664.0 

8908.4 

Pji/ 

12319.2 

10036  .  5 

go/ 

14184.0 

11314.5 

6  4 

16328.5 

12715.3 

6M 

14276.9 

6>2 

16023.6 

6^ 

17966.1 

7 

20140.1 

7K 

22538.4 

25179.6 

182 


MEASUREMENT      OF      GAS      AND      AIR 


Table  37— HOURLY  ORIFICE  COEFFICIENTS  FOR  GAS 

Pressures  taken  2^  diameters  upstream  and  8  diameters  downstream. 
Atmospheric  Pressure  14.7  Ib.        Base  and  Flowing  Temperature  60  deg  fahr. 

Pressure  Base  8  oz.  (15.2  Ib.  Abs.).        Specific  Gravity  .60 

Values  ofCinQ   =C   VhP  where  Q  =  quantity  of  gas   passing  the  orifice 
in  cubic  feet  per  hour. 


DIAMETER 

OF 

DIAMETER  OF 

PIPE  LINE 

ORIFICE 
INCHES 

4" 

6" 

8" 

10" 

K 

5/s 

65.07 
102  2 

64.67 

64.48 

64.42 

% 

7% 

148.1 
203  3 

146.3 

145.7 

145.3 

iu 

268.1 
342.9 

262.1 

260.1 

259.3 

IM 
IH 
1MI 

i% 

428.8 
526.0 
635.9 
760  5 

413.8 
'603.2 

408.7 
592.7 

406.7 
587.8 

IH 
VA 

920.9 
1064  3 

832.9 

813.3 

804.2 

2 

21A 

1246.8 
1454  6 

1105.8 

1071  .  9 

1056.5 

2X 
2*A 

1690.9 
1970  1 

1429.9 

1372.0 

1346.5 

2l/2 
25A 

2270.2 
2625  6 

1810.6 

1713.7 

1674.1 

2% 
27A 

3035.5 
3498  2 

2264.1 

2101.8 

2042.5 

3 

31A 

4031.4 

2797.4 
3433  0 

2542.5 
3039  4 

2452.1 
2900  9 

3H 

4192  7 

3608  6 

3410  2 

m 

4 

5096.2 
6176  9 

4249.7 
4977  8 

3966.7 

4577.7 

4M 
4l| 

7465.2 
8999  4 

5812.4 
6750  6 

5254.2 
6003  .  9 

4M 

7841  8 

6829.1 

5 

9060  0 

7742.9 

5^ 
5^ 
5M 
6 
6M 
6^ 
6^ 
7 
7M 

10488.6 
12116.6 
13950.7 
16060.0 

8761  .  9 
9871.5 
11128.4 
12506.1 
14042.0 
15760.1 
17670.6 
19808.8 
22167.7 

7^ 

24765.5 

183 


MEASUREMENT      OF      GAS      AND      AIR 


Table  38— HOURLY  ORIFICE  COEFFICIENTS  FOR  GAS 

Pressures  taken  2J^  diameters  upstream  and  8  diameters  downstream. 
Atmospheric  Pressure  14.7  lb.        Base  and  Flowing  Temperature  60  deg.  fahr. 

Pressure  Base  10  oz.  (15.325  lb.  Abs.).     Specific  Gravity  .60 

Values  ofCinQ  =C  VhP  where  Q   =  quantity  of  gas  passing  the  orifice 
in  cubic  feet  per  hour. 


DIAMETER 
OF 


DIAMETER  OF  PIPE  LINE 


URIFICE 

INCHES 

4" 

6" 

8" 

10" 

H 

64.54 

64.15 

63.95 

63.89 

H 

101.4 

% 

146.9 

145.1 

144.5 

144.  1 

% 

201.6 

265.9 

260^0 

'258^0 

'257^2 

iy* 

340.1 

m 

425.3 

410.4 

405.4 

'403^3 

i% 

521.7 

.  . 

VA 

630.7 

'598^3 

587.9 

583.0 

1% 

754.3 

•*•/  o 

m 

895.5 

826.1 

806^7 

797.6 

!7/8 

1055.6 

2 

1236.6 

1096.7 

1063.1 

i047^9 

2ys 

1442.7 

21A 

1677.1 

1418.2 

1360^8 

1335.5 

m 

1954.0 

m 

2251.7 

1795^8 

1699^8 

1660^5 

25/8 

2604.2 

&A 

3010.7 

2245^6 

2084^7 

2025^8 

2y8 

3469.6 

3 

3998.5 

2774^5 

2521^7 

2432.1 

&A 

3405.0 

3014.6 

2877.3 

&A 

4158.5 

3579.2 

3382.4 

&A 

5054.6 

4215.1 

3934.4 

4  • 

6126.5 

4937.2 

4540.4 

±1A 

7404.3 

5765.0 

5211.4 

±1A 

8926.0 

6695.5 

5955.0 

4% 

7777.8 

6773.4 

5 

8986.1 

7679.7 

5M 

10403.1 

8690.4 

5^ 

12017.8 

9790.9 

5% 

13836.9 

11037.6 

6 

15929.0 

12404.1 

&A 

13927.5 

Q1A 

15631.5 

u/  A 

6M 

17526.4 

7 

19647.3 

1\4 

21986.9 

1  /4 

VA 

24563.5 

184 


MEASUREMENT      OF      GAS      AND      AIR 


185 


MEASUREMENT      OF      GAS      AND      AIR 

SPECIFIC  GRAVITY 

Specific  gravity  is  the  ratio  between  the  density  of  a 
body  and  the  density  of  some  body  chosen  as  a  standard. 
In  stating  the  specific  gravities  of  gases,  air  is  generally 
taken  as  a  standard.  It  is  very  necessary  to  know  the 
specific  gravity  of  a  gas  when  one  is  measuring  gas  by 
an  orifice  meter. 

The  most  accurate  instrument  for  use  in  obtaining  the 
specific  gravity,  is  the  specific  gravity  balance.  The  effu- 
sion method  cannot  be  relied  upon  for  accurate  determina- 
tions unless  tests  have  been  made  in  comparison  with  the 
specific  gravity  balance  with  various  specific  gravities  of  gas. 
A  complete  description  of  the  methods  and  a  full  set  of 
effusion  method  tables  are  contained  in  our  Hand  Book  of 
Casinghead  Gas. 

MULTIPLIERS    FOR    REVISION    OF    COEFFICIENTS 

It  was  noted  that  each  Table  of  Hourly  Orifice  Co- 
efficients was  calculated  upon  certain  values  for  Base  and 
Flowing  Temperature,  Gravity,  Pressure  Base,  Atmospheric 
Pressure  and  location  of  connections.  It  would  require  a 
library  of  unlimited  size  to  present  coefficients  to  meet  all 
conditions  of  flow  measurement  which  an  orifice  meter  will 
satisfactorily  handle.  In  this  volume  we  present  the  Tables 
of  Hourly  Orifice  Coefficients  which  will  meet  the  most 
frequent  requirements  and  Tables  of  Multipliers  for  use  in 
converting  the  coefficients  to  meet  almost  any  condition. 

Let  Cw  =  new  Coefficient  desired. 

Tbn  =  proposed  new  Base  Temperature  in  degrees 

fahrenheit  absolute. 
Pbn =  proposed  new  Pressure  Base  in  pounds  per 

square  inch  absolute. 
rw  =  new  or  actual  Flowing  Temperature  of  gas 

in  degrees  fahrenheit  absolute. 

186 


MEASUREMENT      OF      GAS      AND      AIR 

GM  =  new  or  actual  Specific  Gravity  of  gas  being 
measured. 

Cn  =  218.6  Cvd2     Tbn_^ 


Cn    218.6  Cvd2TbnPb 


C      218.6  C\ 

ITG 


Therefore,  the  Multiplier  = 


Example — Diameter  of  pipe,  6  inches.  Diameter  of  ori- 
fice, 3  inches. 

Pressure  taken  2]/^  diameters  upstream  and  8 
diameters  downstream. 

Proposed  new  Base  Temperature,  50  deg.  fahr. 
(Tbn  =  5lQ  deg.  absolute). 

Proposed  new  Pressure  Base,  lJ/£  Ib.  above  an 
average  atmosphere  pressure  of  14.4  Ib. 
(Pbn  =  15.9  Ib.  absolute). 

New  or  actual  Flowing  Temperature,  50  deg.  fahr. 
(Tw  =  510  deg.  absolute). 

New  or  actual  Specific  Gravity,  GM  =  0.65 

In  Table  29  the  Coefficient  2902.5  is  based  upon  a  Base 
Temperature  Tb  and  Flowing  Temperature  T  of  60  deg. 
fahr.  (520  deg.  absolute),  Pressure  Base  4  ounces  (Pb  = 
14.65  Ib.  absolute),  and  Specific  Gravity  G=  0.600 

Substituting  these  values  in  the  above  formula. 
510X14.65 


\ 


520X15.9       \510X0.65 

187 


MEASUREMENT      OF      GAS      AND      AIR 

New  Coefficient  Cn  =  2902.5  X  .87679  =  2544.9 
or  using  the  Multiplier  Tables  39,  42,  43  and  45. 

Multiplying  Factor 

Table  42,   50   deg.   Base  Temperature  =.9808 

Table  39,  l}4  Ib.  Pressure  Base  (Coefficient 

in  Table  based  on  4  oz.)  =.9214 

Table  43,  50  deg.  Flowing  Temperature  =  1 . 0098 

Table  45,   Specific   Gravity   .65    (Coefficient 

in  Table  based  on  .600)  =  .  9608 

The  New  Coefficient 

CH  =  2902.5  X  .9808  X  .9214  X 1 .0098  X  .9608  =  2544.9 


Multiplier  for  Change  of  Pressure  Base— 

C    = 


P  P 

^~,  in  which  TT~  ~  is  the  multiplier. 
bn  "bn 


Cn  =  new  or  revised  Coefficient. 

C  =  Coefficient  determined  upon  Pressure  Base  Pb. 

Pb  =  Pressure  Base  in  pounds  per  square  inch  abso- 
lute upon  which  coefficient  C  was  calculated. 

P6n  =  new  or  proposed  Pressure  Base  in  Ib.  per  square 
inch  absolute. 

Example  —  Pressures  taken  2^  diameters  upstream  and 
8  diameters  downstream. 

Pipe  Diameter  =  4  inches.      Base  and  Flowing  Tempera- 

ture =  60  deg.  fahr. 

Orifice  Diameter  =  2  inches.    Atmospheric  Pressure  =  14.4 

Ib. 

Pressure  Base  =  8  ounces.       Specific   Gravity  =  .600. 

188 


MEASUREMENT      OF      GAS      AND      AIR 

The  Coefficient  1293.7  in  Table  29  fulfills  all  conditions 
with  the  exception  of  Pressure  Base  (4  oz.)  upon  which  the 
table  was  prepared. 

In  Table  39  the  Multiplying  Factor  for  8  oz.  Pressure 
Base  =  .9832  (for  converting  Coefficient  from  4  oz.  Pressure 
Base,  14.65  Ib.  absolute,  to  an  8  oz.  Pressure  Base)  which  is 

14.4+0.25     14.65 
equal  to 


Cn=  1293.7  (Orifice  Coefficient  from  Table  29)    X 
.9832=1271.9 

In  case  that  the  atmospheric  pressure  is  different  from 
14.4  and  if  a  different  value  is  specified  in  the  contract,  see 
following  subject. 

Multiplier  for  Atmospheric  Pressure  Changes  — 


Cn  =  C  —  —    —   in  which  —  —  —  -  is  the  multiplier. 
An+pb  An+pb 

CM  =  new  or  revised  Coefficient. 

C  =  Coefficient  based  upon  an  atmospheric  pressure  A  . 

A  =  Atmospheric  Pressure  in  pounds  per  square  inch 
upon  which  the  Orifice  Coefficient  C  was  cal- 
culated. The  value  used  in  Tables  in  this 
book  is  14.4  or  14.7  pounds  per  square  inch. 

pb  =  Pressure  Base  (pressure  expressed  in  pounds  per 
square  inch  above  atmosphere). 

A  „  =  actual  or  new  Atmospheric  Pressure  in  Ib.  per 
square  inch  which  equals  ordinary  Barometer 
reading  in  inches  of  mercury  times  0.4908. 


Example  —  Pressures  taken  2J^  diameters  upstream  and 
8  diameters  downstream. 

189 


MEASUREMENT      OF      GAS      AND      AIR 

Pipe  Diameter  =  4  inches.      Base   Temperature  =  60    deg. 

fahr. 

Orifice  Diameter  =1  inch.      Flowing    Temperature  =     60 

deg.  fahr. 

Pressure  B ase  =  4  oz .  above     Atmospheric  Pressure  =    12.0 
atmospheric  pressure.  Ib. 

Specific  Gravity  =  .600. 

Therefore,  the  proposed  Pressure  Base  is  12.0+ 
0.25  (4  oz.)  =  12.25  Ib.  (absolute). 

The  Coefficient  278.1  in  Table  29  fulfills  all  condi- 
tions with  the  exception  of  the  Atmospheric 
Pressure  (14.4  Ib.)  upon  which  the  Table  was 
calculated. 

In  Table  41  the  Multiplying  Factor  is  1.1959  for  con- 
verting the  Coefficient  from  14.4  Ib.  to  12  Ib.  Atmospheric 
Pressure  at  4  oz.  Pressure  Base. 

_.  14.4+0.25     14.65 

This  factor  1.1959  = = 

12.0+0.25     12.25 

Cn  =  278.1   (Orifice  Coefficient  from  Table  29)    X 
1.1959  =  332.6. 

See  note  at  foot  of  Page  196,  also  Page  221. 

In  cases  where  the  Pressure  Base  also  changes  or  is  dif- 
ferent from  that  of  the  Table, 


A+pb 


The  multiplier  is 


Where  pbn  is  the  new  Pressure  Base  expressed  in 
pounds  per  square  inch  above  the  atmospheric 
pressure. 

190 


MEASUREMENT      OF      GAS      AND      AIR 


Multiplier  for  Base  Temperature  Changes— 

T  T 

Cn  =  C  -~r  ,  in  which  •=—   is  the  multiplier. 
*b  1  b 

Cw  =  new  or  revised  Coefficient. 

C  =  Coefficient  based  upon  Base  Temperature  Tb. 


or  revised  Base  Temperature  in  degrees 
fahrenheit   absolute. 

r6  =  Base  Temperature  upon  which  Coefficient  C  was 
calculated.  Tables  are  usually  prepared  for 
60  deg.  fahr.  (520  deg.  absolute) 

Example  —  Pressures  taken  2J/2  diameters  upstream  and 
8  diameters  downstream. 

Pipe  Diameter  =  8  inches.      Base    Temperature  =  80    deg. 

fahr. 
Orifice  Diameter  =  4  inches.  Flowing  Temperature  =  60 

deg.  fahr. 
Pressure  Base  =  4  ounces.       Atmospheric   Pressure  —  14.4 

Ib. 

Specific  Gravity  =.600. 

The  Coefficient  5165  in  Table  29  fulfills  all  condi- 
tions with  the  exception  of  the  Base  Temper- 
ature (60  deg.  fahr.)  upon  which  the  Table 
was  calculated. 

In  Table  42  the  multiplying  factor  is  1.0385. 

460+80     540 

This  factor  =  -  =  - 

460+60     520 

Cw  =  5165  (Orifice  Coefficient  from  Table  29)  X 
1.0385  =  5363.9 

191 


MEASUREMENT      OF      GAS      AND      AIR 
Multiplier  for  Changes  in  Flowing  Temperature — 

nr  [Y 

Cn  =  C  \~7jT  in  which  \~jT  is  the  multiplier. 

*  *  -*  n 

Cn  =  new  or  revised  Coefficient. 

C  =  Coefficient  calculated  upon  the  Flowing  Tempera- 
ture T. 

T  =  Flowing  Temperature  in  degrees  fahrenheit  ab- 
solute upon  which  the  Coefficient  C  was 
calculated.  Tables  are  usually  prepared 
using  a  Flowing  Temperature  of  60  deg. 
fahr.  (520  deg.  absolute). 

Tn  =  actual  or  new  Flowing  Temperature. 

Example — Pressures  taken  2J/2  diameters  upstream  and 
diameters  downstream. 

Pipe  Diameter  =  6  inches.       Base    Temperature  =  60    deg. 

fahr. 
Orifice  Diameter  =  4  inches.  Flowing  Temperature    =    90 

deg.  fahr. 
Pressure  Base  =  0  pounds.      Atmospheric     Pressure  =  14.4 

Ib. 

Specific  Gravity  =  1.00 

The  Coefficient  5050.4  in  Table  27  fulfills  all  con- 
ditions with  the  exception  of  the  Flowing 
Temperature  which  is  60  deg.  fahr.  In  Table 
43  the  multiplying  factor  is  .9723  for  con- 
verting Coefficient  from  60  deg.  to  90  deg. 
fahr.  Flowing  Temperature. 


^..    ,  460+60         520 

This  factor  =  \—       —  =\  — 
M60+90      X550 

Cn  =  5050.4  (Orifice  Coefficient,  Table  27)  X.9723  = 
4910.5. 

192 


MEASUREMENT      OF      GAS      AND      AIR 
Multiplier  for  Specific  Gravity  Changes — 

r<r  I~G~ 

Cn=  C  \r77~  in  which  \  ~^~  is  the  multiplier. 

\  Gn  \   Gn 

Cn  =  new  or  revised  Coefficient. 

C  =  Coeffiicent  based  upon  Specific  Gravity  G. 

G  =  Specific  Gravity  upon  which  the  Coefficient  C  was 

calculated.      The    Tables  on   Pages  199  and 

,^     200  were  prepared  for  revision  of  Coefficients 

based  on  a  Specific  Gravity  of  1.000  or  .600. 

Gn  =  actual  or  new  Specific  Gravity. 

Example — Pressures  taken  2J/2  diameters  upstream  and 
diameters  downstream. 

Pipe  Diameter  =10  inches.    Base    Temperature  =  60    deg. 

fahr. 

Orifice  Diameter  =  4  inches.  Flowing  Temperature    =    60 

deg.  fahr. 

Pressure  Base  =  0  pounds.      Atmospheric  Pressure  =  14.4 

Ib. 
Specific  Gravity  =1.20 

The  Coefficient  3742.9  in  Table  27  fulfills  all  con- 
ditions with  the  exception  of  the  Specific 
Gravity  which  is  1.00.  In  Table  44  the 
multiplying  factor  is  .9129  for  converting  the 
Coefficient  from  1.00  to  1.20  Specific  Gravity: 


This  f actor  = 


1.20 


CH  =  3742.9  (Hourly  Orifice  Coefficient  from  Table 
27)   X. 9129  =  3416.9. 

193 


MEASUREMENT      OF      GAS      AND      AIR 


194 


MEASUREMENT      OF      GAS      AND      AIR 


Table  39 
PRESSURE  BASE   MULTIPLIERS 

Atmospheric  Pressure  14.4  Ib. 


New 
Pressure  Base 

Table—  0  Ib. 
14.4  Ib.  Abs. 

Table  —  4  oz. 
14.65  Ib.  Abs. 

0  oz. 

1.0000 

1.0173 

4  oz. 

.9829 

1.0000 

8  oz. 

.9664 

.9832 

10  oz. 

.9584 

.9750 

lib. 

.9351 

.9513 

l^lb. 

.9057 

.9214 

21b. 

.8780 

.8933 

3  Ib. 

.8276 

.8420 

Table    40 
PRESSURE    BASE    MULTIPLIERS 

Atmospheric  Pressure  14.7  Ib. 


New 
Pressure  Base 

Table—  0  Ib. 
14.7  Ib.  Abs. 

Table—  4  oz. 
14.95  Ib.  Abs. 

0  oz. 

1.0000 

1.0170 

4  oz. 

.9833 

1.0000 

8  oz. 

.9671 

.9836 

10  oz. 

.9592 

.9755 

1  Ib. 

.9363 

.9522 

81b. 

.8802 

.8952 

31b. 

.8305 

.8446 

When  the  new  Pressure  Base  is  other  than  0  pounds  or  4  oz.  mul- 
tiply the  Coefficient  by  the  proper  Multiplier  in  these  tables  to  revise 
the  Coefficient  for  the  new  Pressure  Base  provided  the  original  Co- 
efficient was  calculated  from  one  of  these  Bases.  Otherwise  use 
formula  on  Page  189. 


195 


MEASUREMENT      OF      GAS      AND      AIR 


Table  41 

MULTIPLIERS  FOR  ATMOSPHERIC 
PRESSURE  CHANGES 

This  Table  is  calculated  for  revision  of  Coefficients  based  on 
Atmospheric  Pressure  14.4  lb.,  plus  a  certain  Pressure  Base  to 
another  Atmospheric  Pressure  plus  the  same  Pressure  Base.  If  the 
gas  is  to  be  calculated  at  a  Base  above  14.4  regardless  of  the 
Atmospheric  Pressure,  do  not  use  this  Table.  See  Page  221. 


Atmos- 
pheric 


PRESSURE  BASE 


Pressure 
Pounds. 

0  oz. 

4  oz. 

;  8  oz. 

10  oz. 

1  lb. 

l^lb. 

2  lb. 

3  lb. 

11.8 

1.2203 

1 
1.2158  1.2114 

1.2093 

1.2031 

1.1955 

1.1884 

1.1757 

12.0 

1.2000  1.1959  1.1920 

1.1901 

1.1846 

1.1778 

1.1714 

1.1600 

12.2 

1.1803  1.1767 

1.1732 

1.1715 

1.1667 

1.1606 

1.1549 

1.1447 

12.4 

1.1613 

1.1581 

1.1550 

1.1536 

1.1493 

1.1439 

1.1389 

1.1299 

12.6 

1.1429 

1.1401 

1.1374 

1.1361 

1.1324 

1.1277 

1.1233 

1.1154 

12.8 

1.1250  1.1226 

1.1203 

1.1192 

1.1159 

1.1119 

1.1081 

1.1013 

13.0 

1.1077  1.1057 

1.1037 

1.1027 

1.1000 

1.0966 

1.0933 

1.0875 

13.2 

1.0909  1.0892 

1.0876 

1.0868 

1.0845 

1.0816 

1.0789 

1.0741 

13.4 

1.0746 

1.0733 

1.0719 

1.0713 

1.0694 

1.0671 

1.0649 

1.0610 

13.6 

1.0588  1.0578 

1.0567 

1.0562 

1.0548 

1.0530 

1.0513 

1.0482 

13.8 

1.0435  1.0428 

1.0420 

1.0416 

1.0405 

1.0392 

1.0380 

1.0357 

14.0 

1.0286  1.0281 

1.0276 

1.0274 

1.0267 

1.0258 

1.0250 

1.0235 

14.2 

1.0141  1.0139 

1.0137 

1.0134 

1.0132 

1.0127 

1.0123 

1.0116 

14.4 

1.0000  1.0000  1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

1.0000 

14.6 

.  9863   .  9865 

.9868 

.9869 

.9872 

.9876 

.9880 

.9886 

14.7 

.  9796   .  9799 

.9803 

.9804 

.9809 

.9815 

.9820 

.9831 

14.8 

.9730 

.9734 

.9739 

.9741 

.9747 

.9755 

.9762 

.9775 

These  factors  apply  to  Atmospheric  Pressure  changes  only.  If 
the  Atmospheric  Pressure  and  the  Pressure  Base  both  change,  make 
the  correction  first  for  Pressure  Base  and  then  for  Atmospheric  Pres- 
sure. To  use  the  Table  of  Pressure  Extensions  set  the  static  pen  arm 
for  Atmospheric  Pressure  reading  above  or  below  the  zero  line  of 
chart  by  the  number  of  pounds  the  Atmospheric  Pressure  is  above  or 
below  14.4  lb.  per  sq.  in.  or  29.3  inches  of  mercury.  If  Atmospheric 
Pressure  is  27.3  inches  of  mercury  or  approximately  13.4  lb.  set  the 
static  pen  arm  to  read  one  lb.  below  zero  reading  when  the  gauge 
lines  are  open.  The  Atmospheric  Pressure  is  expressed  in  pounds  per 
square  inch.  See  Pages  189  and  221. 

196 


MEASUREMENT      OF      GAS      AND      AIR 


Table  42 
BASE  TEMPERATURE  MULTIPLIERS 

Where  the  Base  Temperature  upon  which  the  Coefficients  were 
calculated  was  60  deg.  fahr. 


Degrees 

Multi- 

Degrees 

Multi- 

Degrees 

Multi- 

Fahr. 

plier 

Fahr. 

plier 

Fahr. 

plier 

41 

.9635 

61 

1.0019 

81 

1.0404 

42 

.9654 

62 

1.0038 

82 

1.0423 

43 

.9673 

63 

1.0058 

83 

1.0442 

44 

.9692 

64 

1.0077 

84 

1.0462 

45 

.9712 

65 

1.0096 

85 

1.0481 

46 

.9731 

66 

1.0115 

86 

1.0500 

47 

.9750 

67 

1.0135 

87 

1.0519 

48 

.9769 

68 

1.0154 

88 

1.0538 

49 

.9788 

69 

1.0173 

89 

1.0558 

50 

.9808 

70 

1.0192 

90 

1.0577 

51 

.9827 

71 

1.0212 

91 

1.0596 

52 

.9846 

72 

1.0231 

92 

1.0615 

53 

.9865 

73 

1.0250 

93 

1.0635 

54 

.9885 

74 

1.0269 

94 

1.0654 

55 

.9904 

75 

1.0288 

95 

1.0673 

56 

.9923 

76 

1.0308 

96 

1.0692 

57 

.9942 

77 

1.0327 

97 

1.0712 

58 

.9962 

78 

1.0346 

98 

1.0731 

59 

.9981 

79 

1.0365 

99 

1.0750 

60 

1.0000 

80 

1.0385 

100 

1.0769 

When  the  Base  Temperature  is  greater  or  less  than  60  deg.,  mul- 
tiply the  Coefficient  or  the  result  by  the  Multiplier  opposite  the 
Base  Temperature  in  the  above  Table.  See  Page  191. 


197 


MEASUREMENT      OF      GAS      AND      AIR 

Table  43 
FLOWING    TEMPERATURE     MULTIPLIERS 

Where  the  Flowing  Temperature  upon  which  the   Coefficients  were 
calculated  was  60  deg.  fahr. 


Degrees 
Fahr. 

Multi- 
plier 

Degrees 
Fahr. 

Multi- 
plier 

Degrees 
Fahr. 

Multi- 
plier 

33 

1.0270 

67 

.9933 

0 

1.0632 

34 

1.0260 

68 

.9924 

1 

1.0621 

35 

1.0249 

69 

.9915 

2 

1.0609 

36 

1.0239 

70 

.9905 

3 

1.0598 

37 

1.0229 

71 

.9896 

4 

1.0586 

38 

1.0219 

72 

.9887 

5 

1.0575 

39 

1.0208 

73 

.9877 

6 

1.0564 

40 

1.0198 

74 

.9868 

7 

1.0552 

41 

1.0188 

75 

.9859 

8 

1.0541 

42 

1.0178 

76 

.9850 

9 

1.0530 

43 

1.0167 

77 

.9841 

10 

1.0518 

44 

1.0157 

78 

.9831 

11 

1.0507 

45 

1.0147 

79 

.9822 

12 

1.0496 

46 

1.0137 

80 

.9813 

13 

1.0485 

47 

1.0127 

81 

.9804 

14 

1.0474 

48 

1.0117 

82 

.9795 

15 

1.0463 

49 

1.0107 

83 

.9786 

16 

1.0452 

50 

1.0098 

84 

.9777 

17 

1.0441 

51 

1.0088 

85 

.9768 

18 

1.0430 

52 

1.0078 

86 

.9759 

19 

1.0419 

53 

1.0068 

87 

.9750 

20 

1.0408 

54 

1.0058 

88 

.9741 

21 

1.0398 

55 

1.0048 

89 

.9732 

22 

1.0387 

56 

1.0039 

90 

.9723 

23 

1.0376 

57 

1.0029 

91 

.9715 

24 

1.0365 

58 

1.0019 

92 

.9706 

35 

1.0355 

59 

1.0010 

93 

.9697 

26 

1.0344 

60 

1.0000 

94 

.9688 

27 

1.0333 

61 

.9990 

95 

.9680 

28 

1.0323 

62 

.9981 

96 

.9671 

29 

1.0312 

63 

.9971 

97 

.9662 

30 

1.0302 

64 

.9962 

98 

.9653 

31 

1.0291 

65 

.9952 

99 

.9645 

32 

1.0281 

66 

.9943 

100 

.9636 

When  the  Flowing  Temperature  is  greater  or  less  than  60  deg., 
multiply  the  Coefficient  or  the  result  by  the  Multiplier  opposite  the 
Flowing  Temperature  in  the  above  Table.  See  Page  192. 


198 


MEASUREMENT      OF      GAS      AND      AIR 

Table  44 
SPECIFIC   GRAVITY   MULTIPLIERS 

Where  the  Specific  Gravity  upon  which  the  Coefficients  were 
calculated  was  1.00 


Specific 
Gravity 

Multi- 
plier 

Specific 
Gravity 

Multi- 
plier 

Specific 
Gravity 

Multi- 
plier 

.56 

1.3363 

.91 

1.0483 

1.26 

.8909 

.57 

1.3245 

.92 

1.0426 

1.27 

.8874 

.58 

1.3131 

.93 

1.0370 

1.28 

.8839 

.59 

.3019 

.94 

1.0314 

1.29 

.8805 

.60 

.2910 

.95 

1.0260 

1.30 

.8771 

.61 

.2804 

.96 

1.0206 

1.31 

.8737 

.62 

.2700 

.97 

1.0153 

1.32 

.8704 

.63 

.2599 

.98 

1.0102 

1.33 

.8671 

.64 

.2500 

.99 

1.0050 

1.34 

.8639 

.65 

.2403 

1.00 

1.0000 

1.35 

.8607 

.66 

.2309 

1.01 

.9950 

1.36 

.8575 

.67 

.2217 

1.02 

.9901 

1.37 

.8544 

.68 

1.2127 

1.03 

.9853 

1.38 

.8513 

.69 

1.2039 

1.04 

.9806 

1.39 

.8482 

.70 

1  .  1952 

1.05 

.9759 

1.40 

.8452 

.71 

1.1868 

1.06 

.9713 

1.41 

.8422 

.72 

1.1785 

1.07 

.9667 

1.42 

.8392 

.73 

1.1704 

1.08 

.9623 

1.43 

.8362 

.74 

1  .  1625 

1.09 

.957S 

1.44 

.8333 

.75 

1  .  1547 

1.10 

.9535 

1.45 

.8305 

.76 

1.1471 

1.11 

.9492 

1.46 

.8276 

.77 

1  .  1396 

1.12 

.9449 

1.47 

.824S 

.78 

1.1323 

1.13 

.9407 

1.48 

.8220 

.79 

1.1251 

1.14 

.9366 

1.49 

.8192 

.80 

1.1180 

1.15 

.9325 

1.50 

.8165 

.81 

1.1111 

1.16 

.9285 

1.51 

.8138 

.82 

1.1043 

1.17 

.9245 

1.52 

.8111 

.83 

1.0976 

1.18 

.9206 

1.53 

.8085 

.84 

1.0911 

1.19 

.9167 

1.54 

.8058 

.85 

1.0847 

1.20 

.9129 

.55 

.8032 

.86 

1.0783 

1.21 

.9091 

.56 

.8006 

.87 

1.0721 

1.22 

.9054 

.57 

.7981 

.88 

1.0660 

1.23 

.9017 

.58 

.7956 

.89 

1.0600 

1.24 

.8980 

.59 

.7931 

.90 

1.0541 

1.25 

.8944 

.60 

.7906 

When  the  Specific  Gravity  is  greater  or  less  than  1.00  multiply 
the  Coefficient  by  the  multiplier  opposite  the  new  Specific  Gravity 
if  the  Coefficient  was  based  upon  a  Specific  Gravity  of  1.00.  See 
Page  193. 

199 


MEASUREMENT      OF      GAS      AND      AIR 

Table  45 
SPECIFIC  GRAVITY  MULTIPLIERS 

Where  the  Specific  Gravity  upon  which  the  Coefficients  were 
calculated  was  .600. 


Specific 
Gravity 

Multi- 
plier 

Specific 
Gravity 

Multi- 
plier 

Specific 
Gravity 

Multi- 
plier 

.56 

1.0351 

.91 

.8120 

1.26 

.6901 

.57 

1.0260 

.92 

.8076 

1.27 

.6873 

.58 

1.0171 

.93 

.8032 

1.28 

.6847 

.59 

1.0084 

.94 

.7989 

1.29 

.6820 

.60 

1.0000 

.95 

.7947 

1.30 

.6794 

.61 

.9918 

.96 

.7906 

.31 

.6768 

.62 

.9837 

.97 

.7865 

.32 

.6742 

.63 

.9759 

.98 

.7825 

.33 

.6717 

.64 

.9682 

.99 

.7785 

.34 

.6691 

.65 

.9608 

1.00 

.7746 

.35 

.6667 

.66 

.9535 

1.01 

.7708 

.36 

.6642 

.67 

.9463 

1.02 

.7670 

.37 

.6618 

.68 

.9393 

1.03 

.7632 

.38 

.6594 

.69 

.9325 

1.04 

.7596 

.39 

.6570 

.70 

.9258 

1.05 

.7559 

.40 

.6547 

.71 

.9193 

1.06 

.7524 

1.41 

.6523 

.72 

.9129 

1.07 

.7488 

1.42 

.6500 

.73 

.9066 

1.08 

.7454 

1.43 

.6478 

.74 

.9005 

1.09 

.7419 

1.44 

.6455 

.75 

.8944 

1.10 

.7385 

1.45 

.6433 

.76 

.8885 

1.11 

.7352 

1.46 

.6411 

.77 

.8827 

1.12 

.7319 

1.47 

.6389 

.78 

.8771 

1.13 

.7287 

1.48 

.6367 

.79 

.8715 

1.14 

.7255 

1.49 

.6346 

.80 

.8660 

1.15 

.7223 

1.50 

.6325 

.81 

.8607 

1.16 

.7192 

1.51 

.6304 

.82 

.8554 

1.17 

.7161 

1.52 

.6283 

.83 

.8502 

1.18 

.7131 

1.53 

.6262 

.84 

.8452 

1.19 

.7101 

1.54 

.6242 

.85 

.8402 

1.20 

.7071 

1.55 

.6222 

.86 

.8353 

.21 

.7042 

1.56 

.6202 

.87 

.8305 

.22 

.7013 

1.57 

.6182 

.88 

.8257 

.23 

.6984 

1.58 

.6162 

.89 

.8211 

.24 

.6956 

1.59 

.6143 

.90 

.8165 

.25 

.6928 

1.60 

.6124 

When  the  Specific  Gravity  is  greater  or  less  than  .600  multiply 
the  Coefficient  by  the  multiplier  opposite  the  new  Specific  Gravity 
if  the  Coefficient  was  based  upon  a  Specific  Gravity  of  .600.  See 
Page  193. 

200 


MEASUREMENT      OF      GAS      AND      AIR 


MEASUREMENT      OF      GAS      AND      AIR 

SPECIFICATIONS  FOR  ORIFICE   METER  COMPUTA- 
TIONS FOR  OSAGE  NATION.* 

Symbols  Which  Will  Be  Used  Throughout 

Q  =  Cubic  feet  of  gasper  hour  at  7\,  Pl  or  at  T2,  P2> 
A  =  Affective  area  of  flowing  stream  in  square  feet. 
a  =  Area  of  orifice  in  square  feet. 
C  =  Coefficient   of   contraction,   friction,    etc.     (Vc 

or  Eff.) 

d  =  Diameter  of  orifice  in  inches. 
D  =  Diameter  of  pipe  in  inches. 
V  =  Velocity  of  the  flowing  fluid  feet  per  hour. 
g  =  Acceleration  of  gravity  at  L  and  E. 
H  =  Differential   across   orifice   in   feet   of   flowing 

fluid. 
h  =  Differential  across  orifice  in  inches  of  water  at 

60  deg.  fahr. 
PI=  Absolute  pressure  of  flowing  fluid  pounds  per 

square  inch. 

PZ  =  Absolute  pressure  base  or  (reference  pressure). 
p  =  Atmospheric     pressure     absolute    pounds     per 

square  inch. 

TI=  Absolute  temperature  of  flowing  fluid. 
T2  =  Absolute  temperature  base  or  (reference  tem- 
perature) . 
L  =  Average  latitude  of  the  field  in  which  the  gas 

is  measured. 
E  =  Average  elevation  above  sea  level  of  the  field 

in  which  the  gas  is  measured. 
G  =  Specific   gravity   of   gas   flowing.     (Compared 

to  air  at  14.4  Ib.  and  60  deg.  fahr.) 

X  =  ± 
D 
X  =  The  sign  of  multiplication. 


*  H.  R.  Pierce. 

202 


MEASUREMENT      OF      GAS      AND      AIR 

Assumptions  in  Figuring  Hourly  Gas  Coefficients  to  be  Used 
with  Orifice  Meters. 

Measuring  Gas  in  the  Osage  Nation 

C.  For  orifice  meters  where  differential  taps  are 
taken  1  inch  upstream  from  face  of  orifice  disc 
and  1  inch  from  downstream  face  of  orifice 
disc  and  pressure  connection  taken  from 
downstream  connection,  is  found  from  this 
formula : — 

C  =  .606+1.25  (X-Al)2  Where  X  =  Al  or  more. 
For  any  value  of  X  below  .41,  C  is  equal  to  a 
constant  .606  (by  Weymouth). 

C.  For  orifice  meters  when  differential  taps  are 
taken  2.5  pipe  diameters  above  upstream  face 
of  orifice  disc,  and  downstream  connection 
is  made  8  pipe  diameters  below  upstream 
face  of  disc.  Pressure  connection  taken  at 
upstream  tap. 

C  is  found  from  this  formula; 

C=  (.58925 +.2725^— .825  X2+1.75  X3) 
1  cubic  foot  water  at  60  deg.  fahr.  weighs  62.37  Ib. 
1  cubic  foot  air  at  14.4  Ib.  and  60  deg.  fahr.  weighs 

.0748378  Ib. 

fi2  Q7 

Therefore,  =833.40237  feet  of  air  at  14.4 

.0748378 

and  60  deg.  fahr.  to  equal  in  weight  1    foot 
of  water  at  60  deg.  fahr. 

Therefore,  1  inch  of  water  =  833 '4Q23 '  =  (69.45019 

12 

feet  of  air  at  14.4  Ib.  and   60    deg.  fahr.  to 
equal  in  weight  1  inch  of  water  at  60  deg.  fahr.) 

203 


MEASUREMENT      OF      GAS      AND      AIR 

g=(by  Pierce's    formula)     32.0894    (1  +  .0052375 

Sin  2L)    (I— .00000009575) 
I,  =  36  deg.  45  min.  N.  Latitude  which  is  considered 

the  average  for  the  Osage., 
£=1,000  ft.  above  sea  level,   (considered  average 

elevation  for  Osage) . 
#  =  32.1465. 

/>  =  14.4  Ib.  per  square  inch  absolute. 
P2  =  10  oz.  above  atmospheric  pressure  or  15.025  Ib. 

per   square   inch   absolute.     Considering  the 

average  atmospheric  pressure  to  be  14.4. 
rx  =  60  deg.  fahr.  or  519.6  deg.  absolute  fahr. 
7^  =  60  deg.  fahr.  or  519.6  deg.  absolute  fahr. 

Showing  all  figures  used  in  deduction  of  Air  and  Gas  Con- 
stant to  be  used  in  the  Osage. 

Q  =  AV 
A=aC 

3.1416    d2 


a   = 


4  X  144 


7  =  3600  V2X32.1465# 
14.4 


H  =  h  69.45019 


PI       519.6 

4 


7  =  3600      i2X32.  1465  /*  69.45019     — 


Pl       519.6 


/3.1416  d2\ 
V  4X144  / 

— rr: — \ 

3600  C  ^2X32.1465  //  69.45019  — ) 

X  P!     519.6/ 


204 


MEASUREMENT      OF      GAS      AND      AIR 


Simplifying,  we  get : 

Q  =  218.422  Cd2  \  h  - I 
PI 


T    P 
To  reduce  Q  to  any  desired  P2  or  T2,  we  introduce  —  — 


=  218.422 -2  ^  CW2^U  -1 


T) 

Canceling  —  ,  we  have 
*l 


=   218.422  -?-   Cd2  \lh 
* 


Considering  T2  and  Tlt  60    deg.    fahr.  or  519.6  deg.  ab- 
solute fahr.,  we  have 


Q  =  218.422 


4978.872045014    cd2'  ^h  Pl 


Gravity  of  Gas  1. 
Pressure    Base   of     0   oz.  =  14.4     Ib.    Absolute. 


Q  =  345.755  Cd2  V  h  PI 
Pressure  Base  of    4  oz.    =    14.64  Ib.   Absolute. 


Q  =  340.087  Cd2  V  h  Pl 
Pressure  Base  of  6  oz.  =  14.75  Ib.  Absolute. 

Q  =  337.551  Cd2  V  h  PI 
Pressure  Base  of  8  oz.  =  14.9  Ib.  Absolute. 

Q  =  334.152  Cd2  ^  h  P1 
205 


MEASUREMENT      OF      GAS      AND      AIR 


Pressure  Base  of  10  oz.   =   15.025   Ib.  Absolute. 


Q  =  331.373  Cd2  V  h  Pl 
Pressure  Base    of     1  Ib.     =   15.4   Ib.  Absolute. 


Q  =  323.303  Cd2  V  h  Pl 
Pressure  Base    of     2  Ib.    =    16.4   Ib.  Absolute. 


Q  =  303.590  Cd2  V  h  P± 

To  get  Gas  Constant  divide  air  constant  by  the  square 
root  of  the  gravity  of  gas. 

The  inside  diameter  of  standard  pipe  used  in  orifice 
meter  settings,  as  a  rule,  is  as  follows  :  — 

D  for    4  inch  pipe  =  4.026. 
D  f  or    6  inch  pipe  =  6.  065. 
D  for    8  inch  pipe  =  8.Q71  . 
D  for  10  inch  pipe  =  10.  191. 
D  for  12  inch  pipe  =  12.000. 

Please  note  on  meter  setting  reports  if  other  than  standard 
pipe  is  used  giving  inside  diameter,  weight,  etc. 

In  reporting  size  of  orifice  please  give  nearest  standard 
size  with  the  actual  micrometer  of  orifice  to  ~  inch. 


Special 

For  taps  2.5  and  8  diameters  with  10  oz.  Pressure  Base 
the  one  hour  gas  coefficient  is  derived  from  this  formula  : 

331.373  d2  (.58925+.2725X-.825^2+1.75^3) 


Vspecific  gravity  of  the  gas. 

For  taps  1  inch  and  1  inch  with  10  oz.  Pressure  Base  the 
one  hour  gas  coefficient  is  derived  from  this  formula : 

331.373  d2  [.606+1.25  (  X-Al  )2}" 

Vspecific  gravity  of  the  gas. 
206 


MEASUREMENT      OF      GAS      AND       AIR 


207 


MEASUREMENT      OF      GAS      AND      AIR 


Table  46— VALUES  OF  C,  FOR  2^   AND  8 
DIAMETER  CONNECTIONS 

Diameter  Orifice 


G=.58925+.  2725  ^-. 


X  = 


From  Page  203 


Actual  Internal  Diameter  Pipe 


X 

c. 

X 

c. 

X 

cv 

X 

c. 

.151 

.617612 

.201 

.624903 

.251 

.633345 

.301 

.644251 

.152 

.617755 

.202 

.625056 

.252 

.633534 

.302 

.644503 

.153 

.617897 

.203 

.625209 

.253 

.633735 

.303 

.644757 

.154 

.618040 

.204 

.625364 

.254 

.  633816 

.304 

.  645012 

.155 

.618183 

.205 

.  625518 

.255 

.634109 

.305 

.  645269 

.156 

.  618326 

.206 

.625674 

.256 

.634303 

.306 

.645527 

.157 

.618469 

.207 

.625829 

257 

.634498 

.307 

.645787 

.158 

.618612 

.208 

.625985 

258 

.  634693 

.308 

.  646049 

.159 

.  618755 

.209 

.  626142 

.259 

.  634890 

.309 

.  646312 

.160 

.618898 

.210 

.626299 

.260 

.635088 

.310 

.  646577 

.161 

.619041 

.211 

.626457 

.261 

.  635287 

.311 

.646843 

.162 

.619184 

.212 

.626615 

.262 

.635487 

.312 

.647111 

.163 

.619327 

.213 

.  626774 

.263 

.635688 

.313 

.  647381 

.164 

.619470 

.214 

.626934 

.264 

.635890 

.314 

.  647652 

.165 

.  619613 

.215 

.627094 

.265 

.636094 

.315 

.647925 

.166 

.619756 

.216 

.627255 

.266 

.636298 

.316 

.648199 

.167 

.619900 

.217 

.  627416 

.267 

.636504 

.317 

.648475 

.168 

.  620043 

.218 

.627578 

.268 

.  636711 

.318 

.648753 

.169 

.620187 

.219 

.  627741 

.269 

.636919 

.319 

.649033 

.170 

.620330 

.220 

.627904 

.270 

.637128 

.320 

.649314 

.171 

.  620474 

.221 

.628068 

.271 

.637338 

.321 

.649597 

.172 

.  620618 

.222 

628232 

.272 

.  637549 

.322 

.  649881 

.173 

.620762 

.223 

.628398 

.273 

.637762 

.323 

.650168 

.174 

.620906 

.224 

.628564 

.274 

.637976 

.324 

.650456 

.175 

.621050 

.225 

.628730 

.275 

.638191 

.325 

.650746 

.176 

.621195 

.226 

.628898 

.276 

.638408 

.326 

.  651038 

.177 

.621340 

.227 

.629066 

.277 

.638625 

.327 

.  651331 

.178 

.621485 

.228 

.629235 

.278 

.638844 

.328 

.651626 

.179 

.621630 

.229 

.629404 

.279 

.  639065 

.329 

.651923 

.180 

.  621776 

.230 

.629575 

.280 

.639286 

.330 

.652222 

.181 

.621922 

.231 

.629746 

.281 

.639509 

.331 

.652523 

.182 

.622068 

.232 

.629918 

.282 

.  639733 

.332 

.652825 

.183 

.  622214 

.233 

.630090 

.283 

.639958 

.333 

.653130 

.184 

.622360 

.234 

.630264 

.284 

.640185 

.334 

.653436 

.185 

.622507 

.235 

.630438 

.285 

.640413 

.335 

.653744 

.186 

.622654 

.236 

.630613 

.286 

.  640642 

.336 

.  654054 

.187 

.622802 

.237 

.630789 

.287 

.640873 

.337 

.654365 

.188 

.622950 

.238 

.630966 

.288 

.  641105 

.338 

.  654679 

.189 

.623097 

239 

.631144 

.289 

.  641338 

.339 

.  654995 

.190 

.  623246 

.240 

.631322 

.290 

.641573 

.340 

.655312 

.191 

.623394 

.241 

.631501 

.291 

.641809 

.341 

.655631 

.192 

.623543 

.242 

.631681 

.292 

.  642047 

.342 

.  655953 

.193 

.  623693 

.243 

.631863 

.293 

.  642286 

.343 

.656276 

.194 

.623843 

.244 

.632045 

.294 

.  642526 

.344 

.656601 

.195 

.  623993 

.245 

.632227 

.295 

.642768 

.345 

.656928 

.196 

.624143 

.246 

.632412 

.296 

.643012 

.346 

.657257 

.197 

.  624294 

.247 

.632596 

.297 

.643257 

.347 

.  657589 

.198 

.624446 

.248 

.  632782 

.298 

.643503 

.348 

.657922 

.199 

.624598 

.249 

.632969 

.299 

.643751 

.349 

.  658257 

.200 

.624750 

.250 

.633156 

.300 

.644000 

.350 

.658594 

See  Page   171 

208 


MEASUREMENT      OF      GAS      AND      AIR 


Table  47—  VALUES  OF  Cv  FOR  2y2  AND 
DIAMETER  CONNECTIONS 

C,=.58925+.2725X-.825  *»+1.75  X*     X  =  ^ 

From   Page   203 


Pipe 


X 

cv 

X 

cv 

X 

cv 

X 

c. 

.351 

.658933 

.401 

.678704 

.451 

.704876 

.501 

.738762 

.352 

.659274 

.402 

.679160 

.452 

.705473 

.502 

.739527 

.353 

.659617 

.403 

.679619 

.453 

.706074 

.503 

.740296 

.354 

.659963 

.404 

.680080 

.454 

.706679 

.504 

.741069 

.355 

.  660310 

.405 

.680545 

.455 

.707286 

.505 

.741845 

.356 

.660660 

.406 

.681011 

.456 

.707896 

.506 

.742625 

.357 

.661011 

.407 

.  681481 

.457 

.  708509 

.507 

.  743409 

.358 

.661365 

.408 

.681953 

.458 

.709125 

.508 

.744196 

.359 

.661720 

.409 

.682427 

.459 

.709745 

.509 

.  744987 

.360 

.662078 

.410 

.682904 

.460 

.710368 

.510 

.745782 

.361 

.662438 

.411 

.683384 

.461 

.710994 

.511 

.746580 

.362 

.662800 

.412 

.683866 

.462 

.711623 

.512 

.747382 

.363 

.663165 

.413 

.  684351 

.463 

.712255 

.513 

.748188 

.364 

.  663531 

.414 

.684839 

.464 

.712891 

.514 

.748998 

.365 

.663899 

.415 

.685330 

.465 

.713530 

.515 

.749811 

.366 

.664270 

.416 

.685823 

.466 

.714172 

.516 

.750628 

.367 

.664643 

.417 

.686319 

.467 

.714817 

.517 

.751449 

.368 

.665018 

.418 

.686818 

.468 

.715466 

.518 

.752273 

.369 

.  665396 

.419 

.  687320 

.469 

.716118 

.519 

.753102 

.370 

.665775 

.420 

.687824 

.470 

.716773 

.520 

.753934 

.371 

.666157 

.421 

.688331 

.471 

.717431 

.521 

.754770 

.372 

.666541 

.422 

.688841 

.472 

.718093 

.522 

.755610 

.373 

.666927 

.423 

.689353 

.473 

.718758 

.523 

.756453 

.374 

.667316 

.424 

.689869 

.474 

.719426 

.524 

.757301 

.375 

.667707 

.425 

.  690386 

.475 

.720098 

.525 

.758152 

.376 

.668100 

.426 

.690908 

.476 

.720773 

.526 

.759008 

.377 

.668496 

.427 

.691431 

.477 

.721451 

.527 

.759867 

.378 

.668893 

.428 

.691958 

.478 

.722133 

.528 

.760730 

.379 

.  669293 

.429 

.692487 

.479 

.  722818 

.529 

.761596 

.380 

.669696 

.430 

.693020 

.480 

.723506 

.530 

.762467 

.381 

.670101 

.431 

.693555 

.481 

.  724198 

.531 

.763342 

.382 

.  670507 

.432 

.694093 

.482 

.724893 

.532 

.764220 

.383 

.670917 

.433 

.  694634 

.483 

.725592 

.533 

.765103 

.384 

.671329 

.434 

.  695178 

.484 

.726294 

.534 

.765990 

.385 

.671743 

.435 

.  695724 

.485 

.726999 

.535 

.766880 

.386 

.672160 

.436 

.696274 

.486 

.727708 

.536 

.767775 

.387 

.  672579 

.437 

.696827 

.487 

.728420 

.537 

.768673 

.388 

.673001 

.438 

.697382 

.488 

.729136 

.538 

.769575 

.389 

.  673424 

.439 

.  697941 

.489 

.729855 

.539 

.770482 

.390 

.673851 

.440 

.698502 

.490 

.730578 

.540 

.771392 

.391 

.  674279 

.441 

.699066 

.491 

.731304 

.541 

.772306 

.392 

.674711 

.442 

.  699634 

.492 

.732034 

.542 

.773225 

.393 

.675144 

.443 

.  700204 

.493 

.732768 

.543 

.774147 

.394 

.675580 

.444 

.700777 

.494 

.733504 

.544 

.775074 

.395 

.676019 

.445 

.701354 

.495 

.734245 

.545 

.776004 

.396 

.676460 

.446 

.701933 

.496 

.734989 

.546 

.776939 

.397 

.676904 

.447 

.702516 

.497 

.  735736 

.547 

.777878 

.398 

.  677350 

.448 

.  703101 

.498 

.736487 

.548 

.778821 

.399 

.677799 

.449 

.703690 

.499 

.737242 

.549 

.779768 

.400 

.  678250 

.450 

.704281 

.500 

.738000 

.550 

.  780719 

See  Page   171 

209 


MEASUREMENT      OF      GAS      AND      AIR 


Table  48—  VALUES  OF  Cv  FOR  2^  AND  8 
DIAMETER  CONNECTIONS 

iameter  °Hfice 


G=.58925-K2725  X-.825  XM-1.75  X3    X  = 

From  Pagej203 


Actual  Internal  Diameter  Pipe 


X 

c. 

X 

cv 

X 

cv 

X 

c. 

.551 

.781674 

.601 

.834925 

.651 

.899827 

.701 

.977693 

.552 

.782633 

.602 

.  836104 

.652 

.901253 

.702 

.979391 

.553 

.783597 

.603 

.  837288 

.653 

.902684 

.703 

.981096 

.554 

.784564 

.604 

.838477 

.654 

.  904120 

.704 

.982806 

.555 

.785536 

.605 

.  839671 

.655 

.905562 

.705 

.  984521 

.556 

.786512 

.606 

.840869 

.656 

.907009 

.706 

.  986243 

.557 

.787492 

.607 

.842072 

.657 

.908461 

.707 

.987970 

.558 

.788477 

.608 

.843280 

.658 

.  909918 

.708 

.989703 

.559 

.789465 

.609 

.844492 

.659 

.911380 

.709 

.991442 

.560 

.790458 

.610 

.845709 

.660 

.912848 

.710 

.993187 

.561 

.  791455 

.611 

.  846931 

.661 

.914321 

.711 

.994937 

562 

.  792456 

.612 

.  848158 

.662 

.915799 

.712 

.996693 

.563 

.  793462 

.613 

.849389 

.663 

.917283 

.713 

.998455 

.564: 

.  794472 

.614 

.850626 

.664 

.919772 

.714 

1.000223  , 

.565 

.  795485 

.615 

.851866 

.665 

.920266 

.715 

1.001997 

.566 

.796504 

.616 

.853112 

.666 

.921766 

.716 

1.003777 

.567 

.797527 

.617 

.854363 

.667 

.923271 

.717 

1.005162 

.568 

.798553 

.618 

.855618 

.668 

.  924781 

.718 

1  .  007354 

.569 

.799585 

.619 

.856879 

.669 

.926297 

.719 

1.009151 

.570 

.800620 

.620 

.  858144 

.670 

.927818 

.720 

1.010954 

.571 

.801660 

.621 

.859414 

.671 

.929344 

.721 

1.012763 

.572 

.802704 

.622 

.860689 

.672 

.930876 

.722 

1.014578 

.573 

.803753 

.623 

.861969 

.673 

.932413 

.723 

1.016399 

.574 

.804806 

.624 

.863253 

.674 

.933956 

.724 

1.018226 

.575 

.805863 

.625 

.864543 

.675 

.935504 

.725 

1.020059 

.576 

.806925 

.626 

.865838 

.676 

.937058 

.726 

1.021898 

.577 

.807991 

.627 

.867137 

.677 

.938616 

.727 

1.023742 

.578 

.809062 

.628 

.868441 

678 

.940181 

.728 

1.025593 

.579 

.810137 

.629 

.869751 

.679 

.  941751 

.729 

1.027450 

.580 

.811216 

.630 

.871065 

.680 

.943326 

.730 

1.029312 

.581 

.812300 

.631 

.872384 

.681 

.944907 

.731 

1.031181 

.582 

.813388 

.632 

.  873708 

.682 

.946493 

.732 

1.033056 

.583 

.814481 

.633 

.875037 

683 

.948085 

.733 

1.034936 

.584 

.815578 

.634 

.876371 

.684 

.949683 

.734 

1.036823 

.585 

.816680 

.635 

.877711 

.685 

.951285 

.735 

1.038716 

.586 

.817786 

.636 

.879055 

.686 

.952894 

.736 

1.040615 

.587 

.818897 

.637 

.880404 

.687 

.954508 

.737 

1  .  042520 

.588 

.820012 

.638 

.881758 

.688 

.956127 

.738 

1.044431 

.589 

.821132 

.639 

.883118 

.689 

.957753 

.739 

1.046349 

.590 

.822256 

.640 

.884482 

.690 

.959383 

.740 

1.048272 

.591 

.823385 

.641 

.885851 

.691 

.961019 

.741 

1.050201 

.592 

.824518 

.642 

.887226 

.692 

.962661 

.742 

1.052137 

.593 

.  825656 

.643 

.888606 

.693 

.964309 

.743 

1.054079 

.594 

.826798 

.644 

.  889990 

.694 

.965962 

.744 

1.056027 

.595 

.827945 

.645 

.891380 

.695 

.967621 

.745 

1.057981 

.596 

.  829097 

.646 

.892775 

.696 

.969286 

.746 

1.059941 

.597 

.830253 

.647 

.894175 

.697 

.970956 

.747 

1.061907 

.598 

.831414 

.648 

.895580 

.698 

.  972631 

.748 

1.063880 

.599 

.  832580 

.649 

.896991 

.699 

.974313 

.749 

1.065859 

.600 

.  833750 

.650 

898406 

.700 

.  976000 

.750 

1.067844 

See   Page   171 
210 


MEASUREMENT      OF      GAS      AND      AIR 


Table  49— VALUES  OF   Cv  FOR  FLANGE 
CONNECTIONS 


Cv=. 606+1.25  (X-A1)2 


X  = 


Diameter    of  Orifice 


Actual  Internal   Diameter  of  Pipe 
From   Page  203 


X 

c. 

X 

cv 

X 

Cv 

X 

c. 

.150 

.606000 

.451 

.608101 

.501 

.616351 

.551 

.630851 

.200 

.606000 

.452 

.608205 

.502 

.616,580 

.552 

.631205 

.250 

.606000 

.453 

.  608311 

.503 

.616811 

.553 

.631561 

.300 

.606000 

.454 

.608420 

.504 

.617045 

.554 

.631920 

.350 

.  606000 

.455 

.608531 

.505 

.617281 

.555 

.632281 

.400 

.606000 

.456 

.608645 

.506 

.617520 

.556 

.632645 

.405 

.  606000 

.457 

.608761 

.507 

.617761 

.557 

.633011 

.408 

.606000 

.458 

.608880 

.508 

.618005 

.558 

.633380 

.409 

.606000 

.459 

.609001 

.509 

.  618251 

.559 

.633751 

.410 

.  606000 

.460 

.609125 

.510 

.618500 

.560 

.634125 

.411 

.606001 

.461 

.609251 

.511 

.618751 

.561 

.634501 

.412 

.606005 

.462 

609380 

.512 

.619005 

.562 

.634880 

.413 

.606011 

.463 

.609511 

.513 

.619261 

.563 

.635261 

.414 

.606020 

.464 

.609645 

.514 

.  619520 

.564 

.635645 

.415 

.606031 

.465 

.609781 

.515 

.619781 

.565 

.636031 

.416 

.  606045 

.466 

.609920 

.516 

.620045 

.566 

.636420 

.417 

.  606061 

.467 

.  610061 

.517 

.  620311 

.567 

.636811 

.418 

.606080 

.468 

.610205 

.518 

.620580 

.568 

.  637205 

.419 

.606101 

.469 

.610351 

.519 

.620851 

.569 

.637601 

.420 

.606125 

.470 

.610500 

.520 

.621125 

.570 

.638000 

.421 

.606151 

.471 

.610651 

.521 

.621401 

.571 

.638401 

.422 

.606180 

.472 

.  610805 

.522 

.621680 

.572 

.  638805 

.423 

.606211 

.473 

.610961 

.523 

.621961 

.573 

.639211 

424 

.606245 

.474 

.611120 

.524 

.  622245 

.574 

.639620 

.425 

.  606281 

.475 

.611281 

.525 

.622531 

.575 

.640031 

.426 

.606320 

.476 

.611445 

.526 

.622820 

.576 

.640445 

.427 

.606361 

.477 

.611611 

.527 

.623111 

.577 

.640861 

.428 

.  606405 

.478 

.611780 

.528 

.  623405 

.578 

.641280 

.429 

.606451 

.479 

.611951 

.529 

.623701 

.579 

.641701 

.430 

.  606500 

.480 

.612125 

.530 

.  624000 

.580 

.  642125 

.431 

.606551 

.481 

.612301 

.531 

.624301 

.581 

.642551 

.432 

.  606605 

.482 

.612480 

.532 

.  624605 

.582 

.642980 

.433 

.606661 

.483 

.  612661 

.533 

.624911 

.583 

.643411 

.434 

.  606720 

.484 

.612845 

.534 

.625220 

.584 

.643845 

.435 

.  606781 

.485 

.613031 

.535 

.625531 

.585 

.644281 

.436 

.606845 

.486 

.613220 

.536 

.  625845 

.586 

.644720 

.437 

.606911 

.487 

.613411 

.537 

.  626161 

.587 

.645161 

.438 

.606980 

.488 

.613605 

.538 

.626480 

.588 

.645605 

.439 

.607051 

.489 

.613801 

.539 

.626801 

.589 

.646051 

.440 

.607125 

.490 

.614000 

.540 

.627125 

.590 

.646500 

.441 

.607201 

.491 

.  614201 

.541 

.627451 

.591 

.646951 

.442 

.607280 

.492 

.  614405 

.542 

.627780 

.592 

.647405 

.443 

.607361 

.493 

.614611 

.543 

.628111 

.593 

.647861 

.444 

.  607445 

.494 

.614820 

.544 

.628445 

.594 

.648320 

.445 

.607531 

.495 

.615031 

.545 

.  628781 

.595 

.  648781 

.446 

.607620 

.496 

.615245 

.546 

.629120 

.596 

.649245 

.447 

.607711 

.497 

.615461 

.547 

.  629461 

.597 

.649711 

.448 

.607805 

.498 

.615680 

.548 

.629805 

.598 

.650180 

.449 

.607901 

.499 

.615901 

.549 

.630151 

.599 

.650651 

.450 

-.608000 

.500 

.616125 

.550 

.630500 

.600 

.651125 

211 


MEASUREMENT      OF      GAS      AND      AIR 


Table  50— VALUES  OF  Cv  FOR  FLANGE 


CONNECTIONS 


C9  =  .606  +  1.25  (X-Al)2       X  = 


Diameter  of  Orifice 


From  Page  203 


Actual  Internal  Diameter  of  Pipe 


X 

c. 

X 

cv 

X 

c, 

.601 

.651601 

.651 

.678601 

.701 

.711851 

.602 

.652080 

.652 

.679205 

.702 

.712580 

.603 

.652561 

.653 

.679811 

.703 

.713311 

.604 

.653045 

.654 

.680420 

.704 

.  714045 

.605 

.653531 

.655 

.681031 

.705 

.714781 

.606 

.  654020 

.656 

.681645 

.706 

.715520 

.607 

.654511 

.657 

.682261 

.707 

.716261 

.608 

.655005 

.658 

.682880 

.708 

.717005 

.609 

.  655501 

.659 

.683501 

.709 

.717751 

.610 

.656000 

.660 

.684125 

.710 

.718500 

.611 

.656501 

.661 

.684751 

.711 

.  719251 

.612 

.657005 

.662 

.685380 

.712 

.  720005 

.613 

.657511 

.663 

.686011 

.713 

.720761 

.614 

.658020 

.664 

.686645 

.714 

.721520 

.615 

.658531 

.665 

.687281 

.715 

.  722281 

.616 

.  659045 

.666 

.687920 

.716 

.723045 

.617 

.659561 

.667 

.688561 

.717 

.723811 

.618 

.660080 

.668 

.689205 

.718 

.724580 

.619 

.  660601 

.669 

.  689851 

.719 

.725351 

.620 

.661125 

.670 

.690500 

.720 

.726125  ' 

.621 

.661651 

.671 

.691151 

.721 

.  726901 

622 

.662180 

.672 

.691805 

.722 

.727680 

.623 

.662711 

.673 

.  692461 

.723 

.  728461 

.624 

.  663245 

.674 

.693120 

.724 

.729245 

.625 

.663781 

.675 

.  693781 

.725 

.  730031 

.626 

.  664320 

.676 

.694445 

.726 

.730820 

.627 

.  664861 

.677 

.695111 

.727 

.731611 

.628 

.665405 

.678 

.  695780 

.728 

.  732405 

.629 

.  665951 

.679 

.696451 

.729 

.733201 

.630 

.666500 

.680 

.697125 

.730 

.734000 

.631 

.667051 

.681 

.697801 

.731 

.734801 

.632 

.  667605 

.682 

.698480 

.732 

.735605 

.633 

.  668161 

.683 

.699161 

.733 

.736411 

.634 

.  668720 

.684 

.699845 

.734 

.737220 

.635 

.669281 

.685 

.700531 

.735 

.738031 

.636 

.669845 

.686 

.  701220 

.736 

.738845 

.637 

.670411 

.687 

.701911 

.737 

.  739661 

.638 

.670980 

.688 

.702605 

.738 

.740480 

.639 

.  671551 

.689 

.703201 

.739 

.741301 

.640 

.672125 

.690 

.  704000 

.740 

.742125 

.641 

.672701 

.691 

.  704701 

.741 

.742951 

.642 

.673280 

.692 

.  705405 

.742 

.743780 

.643 

.673861 

.693 

.706111 

.743 

.744611 

.644 

.674445 

.694 

.706820 

.744 

.745445 

.645 

.675031 

.695 

.707531 

.745 

.746281 

.646 

.675620 

.696 

.708245 

.746 

.747120 

.647 

.676211 

.697 

.708961 

.747 

.747961 

.648 

.  676805 

.698 

.709680 

.748 

.748805 

.649 

.677401 

.699 

.  710401 

.749 

.749651 

.650 

.678000 

.700 

.711125 

.750 

.750500 

212 


MEASUREMENT      OF      GAS      AND      AIR 


Table  51— HOURLY  ORIFICE  COEFFICIENTS 
FOR  GAS  AND  AIR 

Pressures  taken  at  Flanges,  Standard  Pipe,  Page  206. 
Atmospheric  Pressure  14.4  Base  and  Flowing  Temperature  60  deg.  fahr. 

Pressure  Base  0  Ib.  Specific  Gravity  1.000 


Diameter 
of  Orifice 
Inches 

DIAMETER  OF  PIPE  LINE 

4" 

6" 

8" 

10" 

12" 

H 

52.3819 

52.3819 

52.3819 

52.3819 

52.3819 

5A 

81.8467 

81.8467 

81.8467 

81.8467 

81.8467 

% 

117.859 

117.859 

117.859 

117.859 

117.859 

% 

160.430 

160.420 

160.420 

160.420 

160.4120 

I 

209.528 

209.538 

209.528 

209.528 

209.528 

VA 

265.183 

265.183 

265.183 

265.183 

265.183 

VA 

327.387 

327.387 

327.387 

327.  387 

327.387 

m 

396.138 

396.138 

396.138 

396.138 

396.138 

VA 

471.437 

471.437 

471.437 

471.437 

471.437 

i*A 

553.283 

553.283 

553.283 

553.283 

553.283 

IH 

642.484 

641.678 

641.678 

641.678 

641.678 

VA 

741.338 

736.620 

736.620 

736.620 

736.620 

2 

851.136 

838.110 

838.110 

838.110 

838.110 

zy* 

973.238 

946.148 

946.148 

946.148 

946.148 

21A 

1109.22 

1060.74 

1060.74 

1060.74 

1060.74 

2*A 

1260.77 

1181,86 

1181.86 

1181.86 

1181.86 

2y2 

1429.76 

1309.56 

1309.55 

1309.55 

1309.55 

25A 

1618.20 

1445.33 

1443.78 

1443.78 

1443.78 

&A 

1828.25 

1590.71 

1584.55 

1584.55 

1584.55 

27A 

2062.25 

1746.52 

1731.88 

1731.88 

1731.88 

3 

2322.68 

1913.62 

1885.75 

1885.75 

1885.75 

3M 

2285.45 

2213.14 

2213.14 

3213.14 

31A 

2714.51 

2569.67 

2566.71 

3566.71 

VA 

3210.19 

2964.62 

2946.48 

3946.48 

4 

3782.97 

3403.11 

3352.44 

3353.44 

4M 

4444.48 

3890.68 

3784.97 

3784.59 

4^ 

5207.37 

4433.47 

4251.65 

4343.93 

*H 

5038.25 

4758.16 

4727.47 

5 

5712.42 

5308.43 

5268.67 

5M 

6463.97 

5906.84 

5784.11 

VA 

7301.55 

6558.11 

6368.75 

&A 

8234.42 

7267.37 

6995.86 

6 

9272.46 

8040.14 

7669.03 

6M 

8882.33 

8393.05 

VA 

9800.26 

9169.10 

6M 

10800.57 

10004  .  55 

v'X'± 

7 

11890.4 

10903.11 

?M 

13077.1 

11869.7 

VA 

14368.7 

13909.7 

8 

15331.9 

&A 

17917.6 

9 

31018.7 

Based  on  345.755  d2[-606  +1.25  (Z-.41)2] 
213 


Page  205. 


MEASUREMENT       OF      GAS      AND      AIR 


INCHES  MERCURY  VACUUM 


GAUGE 


PRESSURE  -POUNDS 


LINE  PRESSUR^ 


MAXIMUM  CAPACITY  OF  20    DIFFERENTIAL  GAUGE 
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DIAMETERS  OF  ORIFICES -INCHES 


MEASUREMENT      OF      GAS      AND      AIR 


2      -s     s    3 


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DIAMETERS  QF  ORIFICES  -  INCHES 


215 


MEASUREMENT      OF      GAS      AND       AIR 


INCHES  MERCURY  VACUUM  GAUGE  PRESSURE -POUNDS 

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Based  on  following  conditions 

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PRESSURE  BASE  0  Ib. 

1ERIC  PRESSURE  14.4  Ibs. 

SPECIFIC  GRAVITY  1.00 

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216 


MEASUREMENT      OF      GAS      AND      AIR 


i          ?        1      a    s    g   §      §     §    5    g 

GAUGE  PRESSURE -POUNDS 
LINE  PRESSURE 


i 

CJ 

UJ 


J| 

2  >• 


"1  1  Si  Jf 

j!*  4       &-S       11 

*ij   u   ;i 


•*.  3 


Slflli 


MAXIMUM  CAPACITY  OF  100    DIFFERENTIAL  GAUGE 
CUBIC  FT.  PER  HOUR 

Jo  oooo    o  ooooo  oooog  Sogoo 

,ooS  ggggg  §  ggggg  gSSSS  gSSSS   g  gggSS  Sgggg  ggggg 

)   000      00000       O      00000      00000     00  000       0     O   0000     O    O  OOO      00000 

,000    ~1»»0     u,    ou.0,5000002,.,5.20     «   oujo.no   ooooo   ~l«»o 


I1II  IIHi  IH 

MAXIMUM  CAPACITY  OF  50    DIFFERENTIAL  GAUGE 
DIAMETERS  OF  ORIFICES -INCHES 


217 


MEASUREMENT      OF      GAS      AND      AIR 


Fig.  83—20  INCH  DIFFERENTIAL  GAUGE 


218 


MEASUREMENT      OF      GAS      AND      AIR 

MEASURING  GAS   IN   LARGE   VOLUMES* 

"The  following  information  was  compiled  from  records 
obtained  under  ordinary  operating  conditions. 

Data  obtained  at  the  city  gates  of  Lawrence,  Kansas, 
where  the  Kansas  Natural  Gas  Company  maintains  two 
orifice  meter  settings — one  in  a  6  inch  line  and  the  other  in 
an  8  inch  line: — After  the  gas  passes  through  the  orifice 
meters  it  is  again  measured  through  a  100,000  cu.  ft.  per 
hour  Thomas  electric  meter  and,  covering  a  period  of  444 
days,  there  was  342,156,000  cu.  ft.  registered  through  the 
orifice  meters,  343,108,000  cu.  ft.  registered  through  the 
Thomas  electric  meter,  a  difference  of  952,000  cu.  ft.,  or  a 
difference  in  percentage  of  0.28  (twenty-eight  one-hundredths 
of  one  per  cent). 

Data  which  was  obtained  at  the  city  gates  of  Leaven- 
worth,  Kansas,  where  the  Kansas  Natural  Gas  Company 
maintains  a  10  inch  orifice  meter  setting: — After  the  gas 
passes  through  the  orifice  meter  it  is  then  measured  through 
a  100,000  cu.  ft.  per  hour  Thomas  electric  meter  and,  cover- 
ing a  period  of  252  days,  there  was  186,251,000  cu.  ft.  regis- 
tered through  the  orifice  meter,  and  185,969,000  cu.  ft. 
registered  through  the  Thomas  electric  meter,  a  difference 
of  282,000  cu.  ft.  or  a  difference  in  percentage  of  0.15  (fifteen 
one-hundredths  of  one  per  cent). 

Comparative  runs  under  ordinary  operating  conditions, 
at  a  4  inch  orifice  meter  setting  measuring  gas  to  an  isolated 
portion  of  the  Wyandotte  County  Gas  Company's  distri- 
bution system  in  Rosedale,  Kansas,  supplying  about  two 
hundred  domestic  consumers : — -After  the  gas  passed  through 
the  orifice  meter  it  was  again  measured  through  three  60-A 
tin  meters  (1800  cu.  ft.  per  hour  each)  and,  covering  a  period 
of  120  days,  there  was  registered  by  the  orifice  meter  4,553,- 
840  cu.  ft.,  and  through  the  three  60-A  tin  meters  4,480,380 
cu.  ft.,  a  difference  of  73,460  cu.  ft.,  or  a  difference  in  per- 

*  By  V.  C.  Jarboe 

219 


MEASUREMENT      OF      GAS      AND      AIR 

centage  of  1.61  (one  and  sixty-one one-hundredths  percent). 
The  differential  carried  on  this  orifice  meter  varied  from  2 
inches  at  night  to  about  48  inches  during  the  peak,  or  meal- 
time load. 

Taking  into  consideration  the  figures  closed  as  of  Feb- 
ruary 25th,  1922,  at  the  city  gates  of  Lawrence,  Kansas, 
covering  a  period  of  750  days,  the  orifice  meters  registered 
547,759,000  cu.  ft.,  the  Thomas  meter  548,417,000  cu.  ft., 
a  difference  of  658,000  cu.  ft.  or  a  difference  in  percentage  of 
0.12  (twelve  one-hundredths  of  one  per  cent). 

The  figures  closed  as  of  February  25th,  1922,  at  the  city 
gates  of  Leavenworth,  Kansas,  covering  a  period  of  527 
days,  the  orifice  meter  registered  357,978,000  cu.  ft.,  the 
Thomas  meter  357,961,000  cu.  ft.,  a  difference  of  17,000 
cu.  ft. 

During  all  of  this  operation  the  meters  were  given  the 
ordinary  attention  that  meters  should  be  given  in  order  to 
get  dependable  measurements. 

The  Thomas  meters  referred  to  above  are  the  property  of 
the  Lawrence  and  Leavenworth  Gas  Companies,  and  the 
three  60-A  tin  meters  are  the  property  of  the  Wyandotte 
County  Gas  Company." 


10A.M. 


Fig.  8J— SECTION  OF  10  INCH,  10  LB.  ORIFICE  METER  CHART 


220 


MEASUREMENT      OF      GAS      AND      AIR 

EFFECT    OF    ATMOSPHERIC    PRESSURE    ON    GAS 
MEASUREMENT 

The  volume  of  gas  measured  is  expressed  at  a  certain 
pressure  base,  which  is  usually  designated  as  a  certain  number 
of  ounces  or  pounds  per  square  inch.  This  pressure  is  the 
gauge  pressure  above  the  atmospheric  pressure  at  the  point 
of  measurement  unless  otherwise  designated  by  contract  or 
common  understanding. 

The  standard  practice  has  been  to  consider  atmospheric 
pressure  as  14.4  Ib.  per  square  inch.  While  it  is  true  that 
this  value  is  a  representative  one  for  most  of  the  gas  fields, 
gas  is  being  produced  in  large  volumes  in  locations  of  high 
altitude  where  the  pressure  of  the  atmosphere  is  11.9  pounds 
per  square  inch  and  even  less. 

Where  the  atmospheric  pressure  is  14.4  Ib.  per  square 
inch  and  gas  is  measured  at  an  8  ounce  base,  the  total  or 
absolute  pressure  base  in  pounds  per  square  inch,  is  14.4  Ib. 
plus  8  ounces  (0.5  Ib.)  or  14.9  Ib.  per  square  inch.  However, 
at  11.9  Ib.  atmospheric  pressure,  the  same  8  ounce  pressure 
base  represents  an  absolute  pressure  of  11.9  Ib.  plus  8  ounces 
(0.5  Ib.)  or  12.4  Ib.  per  square  inch,  s,o  that  with  temperature 
conditions  similar,  the  weight  of  gas  in  a  cubic  foot  in  the 
first  instance  is  approximately  20  per  cent  greater  than  in 
the  second. 

If  the  gas  being  produced  at  the  higher  altitude  were 
piped  to  a  lower  altitude,  the  calculated  volume  decreases  if 
the  same  pressure  base  is  used  for  measurement  above  the 
atmospheric  pressure  at  each  point.  Using  the  two  values 
above  cited,  600,000  cu.  ft.  measured  at  8  oz.  above  11.9  Ib. 
atmospheric  pressure  would  become  only  500,000  cu.  ft.  at 
the  14.4  Ib.  pressure  at  an  8  ounce  base.  The  weight  does 
not  change  neither  does  the  heat  content. 

The  value  of  gas  consists  mainly  of  its  heat  producing 
quality.  Although  it  is  not  purchased  or  sold  on  this  basis 
directly,  this  condition  is  approached  in  high  pressure  meas- 

221 


MEASUREMENT      OF      GAS      AND      AIR 


Fig.   85— ORIFICE    METER   INSTALLATION,   FLANGE 
TAP   CONNECTIONS 


222 


MEASUREMENT      OF      GAS      AND      AIR 

urement,  by  contract  requirements  of  a  certain  pressure  base 
and  base  temperature  at  which  the  volume  shall  be  calculated. 
If  all  gas  had  the  same  specific  gravity  the  above  method  of 
measurement  would  insure  the  same  weight  of  gas  in  each 
cubic  foot.  However,  the  heat  content  varies  with  the 
chemical  constituents  of  the  gas,  so  that  the  only  manner  in 
which  gas  could  be  sold  on  a  heat  or  B.  t.  u.  basis  would  be 
to  have  a  combustion  analysis  made.  Such  an  analysis  is 
not  usually  made  but  for  practical  purposes  gas  and  fuel  oil 
are  used  under  the  same  or  similar  boilers  at  the  same  load 
to  determine  the  relative  economy  of  the  two  fuels. 

A  barrel  of  fuel  oil  will  weigh  nearly  the  same  regardless 
of  atmospheric  pressure  so  that  in  comparing  fuel  oil  with 
gas  it  is  necessary  to  know  the  absolute  pressure  under  which 
the  gas  volume  is  expressed.  If  the  gas  measured  at  8 
ounces  above  a  atmosphere  of  11.9  Ib.  or  12.4  Ib.  per  square 
inch  absolute  contained  800  B.  t.  u.  per  cubic  foot,  the  same 
gas  measured  at  8  ounces  above  14.4  or  14.9  Ib.  absolute 
would  contain  960  B.  t.  u.  per  cubic  foot.  Assuming  the 
barrel  of  fuel  oil  contained  4,800,000  B.  t.  u.  it  would  be 
equivalent  to  6,000  cu.  ft.  measured  at  12.4  Ib.  absolute  and 
5,000  cu.  ft.  measured  at  14.9  absolute.  So  that  in  making 
comparisons,  the  atmospheric  pressure  may  become  an  im- 
portant factor. 

The  above  examples  illustrate  what  an  important  part 
atmospheric  pressure  plays  in  gas  measurement  at  high 
altitudes. 

For  purposes  of  comparison  gas  must  be  calculated  on 
the  same  absolute  pressure  base.  The  Department  of  In- 
terior have  issued  regulations  in  regard  to  this  subject  in 
"Regulations  to  Govern  the  Production  of  Oil  and  Gas,"* 
which  provides  that  all  gas  must  be  reported  on  a  base  of 
10  oz.  above  an  atmospheric  pressure  of  14.4  Ib.  per  sq.  in. 
or  15.025  Ib.  absolute.  The  effect  of  the  atmospheric  pres- 

*  See  Page  232 

223 


MEASUREMENT      OF      GAS      AND      AIR 

sure  on  the  absolute  pressure  base  only  affects  the  value  of 
the  Coefficient.  If  the  atmospheric  pressure  varies  from  14.4 
and  it  is  desired  to  measure  the  gas  at  a  certain  number  of 
ounces  or  pounds  above  the  atmosphere,  the  Coefficient 
must  be  revised  if  it  was  derived  by  using  14.4  as  the  at- 
mospheric pressure,  for  the  Coefficient  C  is  equal  to  :  — 


Where  P&  is  the  pressure  base  in  pounds  per  square  inch 
absolute.  It  is  readily  seen  that  as  Pb  decreases  in  value; 
C  increases,  and  consequently  the  calculated  volume  in- 
creases. The  formula  for  revision  of  the  Coefficient  is  given 
on  Page  189  and  Table  of  Multipliers  on  Page  196. 

When  it  is  desired  to  measure  gas  at  a  pressure  base  above 
a  pressure  of  14.4  so  that  the  volume  would  be  equal  to  that 
which  would  occur  if  the  pressure  were  14.4  regardless  of  the 
atmospheric  pressure  at  point  of  measurement,  then  the 
Coefficient  should  not  be  revised,  on  account  of  the  different 
atmospheric  pressure,  if  the  Coefficient  was  derived  by  using 
14.4.  The  reader  is  referred  to  Contracts,  Page  230,  for  in- 
terpretations of  various  phrases  regarding  pressure  base  and 
atmospheric  pressure. 

In  addition  to  the  effect  on  the  basis  of  measurement, 
the  pressure  of  the  atmosphere  also  affects  the  quantity  due 
to  the  absolute  pressure  of  the  gas  being  measured.  The 
quantity  of  gas  when  measured  by  an  orifice  meter  is 


where  Q  =  quantity  in  cubic  feet  per  hour  passing  the 

orifice. 

C  =  Hourly  Orifice  Coefficient  of  the  orifice.     The 
value  of  this  term  is  affected  by  the  pressure 
base  and  any  factor  which  affects  the  value  of 
the  pressure  base  in  absolute  units. 
h  =  differential  in  inches  of  water. 

224 


MEASUREMENT      OF      GAS      AND      AIR 

P  =f  Static  or  line  pressure  expressed  in  pounds  per 
square  inch  absolute  which  is  the  atmospheric 
pressure  plus  or  minus  the  gauge  pressure.* 

The  static  pressure  or  line  pressure  in  pounds  per  square 
inch  or  in  inches  of  mercury  vacuum  is  usually  recorded 
on  the  same  chart  as  the  differential  pressure. 

When  orifice  meters  were  first  commercially  used,  the 
average  atmospheric  pressure  of  all  the  gas  fields  was  14.4 
Ib.  and  this  value  was  used  and  is  still  used  in  the  preparation 
of  tables  of  Pressure  Extensions,  which  tables  give  the  values 
of  ^IhP  for  various  values  of  differential  in  combination  with 
various  pressures.  In  these  tables  P  is  equal  to  14.4  plus  the 
gauge  pressure,  and  in  cases  of  vacuum  lines,  P  equals  14.4 
minus  .4908  times  inches  of  mercury  vacuum.  14.4  Ib.  is 
considered  the  atmospheric  pressure. 

It  is  readily  understood  that  if  the  atmospheric  pressure 
varies  from  14.4,  the  volume  will  be  affected.  For  example, 
if  the  gas  is  flowing  under  an  atmospheric  pressure  of  11.9 
or  2.5  Ib.  below  14.4  and  the  static  pen  rested  at  zero  without 
any  previous  adjustment,  the  pressure  on  the  gas  would  be 
equivalent  to  a  minus  pressure  or  5  inches  vacuum  below 
an  absolute  pressure  of  14.4  Ib. 

If  the  tables  of  Pressure  Extensions  are  used  without  any 
adjustment  for  change  of  atmospheric  pressure  the  error  in 
this  case  is  V(14.4+0)&  compared  with  V(11.9+0)&  or 
3.795/z  compared  with  3.456/z,  being  10  per  cent  error.  At 
125  Ib.  the  error  is  about  1  per  cent  V(14.4+125)A=11.81A, 
and  V(11.9+125)A=11.70&.  At  500  Ib.  the  error  is  one- 
fourth  per  cent.  However,  under  a  vacuum  the  error  in- 
creases as  the  vacuum  increases.  At  20  inches  of  mercury 
vacuum  the  error  is  46  per  cent. 


V(14.4  -.4908  X  20)  h  =  2.\4h 
V(l  1.9 —.4908X20)  A  =  1  .46  A 


*  See  Page  169. 

225 


MEASUREMENT      OF      GAS      AND      AIR 

The  book  of  Pressure  Extensions  may  be  used  by  making 
adjustments  either  to  the  readings  or  to  the  static  gauge. 

When  the  atmospheric  pressure  is  less  than  14.4  make  a 
deduction  from  the  static  reading  equal  to  the  amount  that 
the  atmospheric  pressure  is  less  than  14.4.  For  example, 
where  the  atmospheric  pressure  is  2.5  Ib.  less  than  14.4  or 
11.9  Ib.  subtract  2.5  Ib.  from  all  gauge  readings.  When  the 
gauge  reading  for  a  period  is  20.5  Ib.  and  differential  is  30 
inches,  look  up  the  extension  of  20.5 — 2.5  Ib.  or  18  Ib.,  and 
30  inches  differential.  This  method  may  be  proved  thus : 


V(11.9+20.5)30=  V(14.4+18)30 


V32.4X30     =      V32.4X30 

In  cases  of  vacuum,  add  numerically  to  the  gauge  reading  in 
inches  of  mercury,  the  difference  between  29.3  inches  mer- 
cury (14.4  Ib.)  and  the  barometric  reading.  If  the  baromet- 
ric reading  is  24.3  inches  (11.9  Ib.)  the  difference  is  5  inches, 
then  if  the  static  reading  is  20  inches  and  the  differential  is 
10  inches,  to  obtain  proper  volume  for  the  period  look  up  the 
extension  of  20  plus  5  or  25  inches  of  mercury  vacuum  and 
10  inches  differential. 


For  V(l  1.9  -.4908X20)  10=  V  (14.4 -.4908X25)  10 


V(H.9-9.8)10=  V(14.4-12.3)10 


V2.1X10  =  V2.1X10 

Adjustments  may  be  made  on  the  gauge  to  save  all  office 
work.  When  the  atmospheric  pressure  is  less  than  14.4,  install 
the  recording  differential  and  static  gauge  with  the  static  pen 
located  a  space  below  the  zero  line  equal  to  the  number 
of  pounds  that  the  pressure  of  the  atmosphere  is  less  than 
14.4.  Thus,  when  the  atmospheric  pressure  is  11.9  set  the 
static  pen  2.5  Ib.  below  zero  when  the  gauge  is  open  to 

226 


MEASUREMENT      OF      GAS      AND      AIR 

the  air.  When  a  pressure  acts  on  the  gauge  and  the  gauge 
registers  0,  the  absolute  pressure  will  be  11.9+2.5  or  14.4 
which  corresponds  to  the  absolute  pressure  for  0  Ib.  in  the 
pressure  extension  tables.  Where  the  reading  is  10  Ib.  the 
absolute  pressure  registered  by  the  pen  is  12.5+11.9  =  24.4 
Ib.  per  square  inch  absolute,  which  is  the  absolute  pressure 
corresponding  to  10  Ib.  in  the  Pressure  Extension  Book. 
Gauges  on  vacuum  lines  are  adjusted  in  a  similar  manner. 
If  the  barometer  reading  is  24.3  inches  (11.9  Ib.)  which  is 
5  inches  of  mercury  less  than  29.3  inches  (14.4  Ib.)  set  the 
pen  at  5  inches  of  mercury  vacuum  (below  the  zero  line) 
when  the  gauge  is  installed  or  when  open  to  the  atmosphere. 
When  the  chart  reading  is  20  inches  of  vacuum  the  pressure  is 
15  inches  below  the  atmosphere  (24.3  less  15)  or  9.3  inches 
absolute  which  is  the  same  absolute  pressure  used  in  cal- 
culating the  pressure  extension  (29.3 — 20  =  9.3)  except  that 
this  value  is  expressed  in  pounds  in  making  the  calculations. 
When  the  atmospheric  pressure  is  greater  than  14.4  adjust- 
ments are  made  in  the  opposite  manner.  For  instance  if  the 
atmospheric  pressure  is  14.7  Ib.  add  0.3  Ib.  to  the  static 
pressure  readings  before  looking  up  the  extensions.  If  on  a 
vacuum  line  subtract  0.6  inches  of  mercury  from  the  gauge 
reading  before  obtaining  the  extension.  If  it  is  desired  to 
have  the  change  made  by  the  gauge  so  as  to  use  the  Pressure 
Extension  Tables  without  any  further  trouble  set  the  static 
pen  to  read  0.3  Ib.  or  0.6  inches  of  mercury  above  the  zero 
when  the  gauge  is  open  to  the  atmosphere. 

Do  not  make  revisions  to  both  the  readings  and  the 
gauge  but  only  to  the  one  or  the  other.  When  adjustments 
are  made  notations  should  be  shown  on  charts  and  reports 
so  that  checkers  may  be  able  to  make  calculations  in  proper 
manner. 

From  the  preceding  discussion  it  will  be  noted  that  the 
effect  of  the  atmospheric  pressure  on  the  pressure  base, 
creates  a  constant  percentage  deviation  on  the  quantity 

227 


MEASUREMENT      OF      GAS      AND      AIR 

and  the  effect  on  the  static  pressure  is  variable.  The  follow- 
ing examples  indicate  the  varying  results  which  may  be  ob- 
tained from  the  same  data. 

Gas  being  measured  with  pressure  connections  at  2J4 
and  8  diameters  from  the  orifice.     Period  one  day. 

Size  of  line,  8  inches.  Diameter  of  Orifice,  6  inches. 

Pressure  Base,  4  oz.  Specific  Gravity,  .600. 

Atmospheric  Pressure  12.4  Ib.  Temperature  60  deg.  fahr. 
Unrevised  Hourly  Coefficient  is  16664,  see  Page  175. 
Average  Gauge  Pressure  10  Ib. 
Average  Differential  Pressure  16  inches. 
Gauge  not  adjusted. 

(1)  Coefficient  revised,  Pressure  Extensions  not  revised. 

(14  4-1-  25)  *      

£  =  24X16664)-        '—£     V  (14.4  +  10)  16  =  9,152,000  cu. 

\LZA-\-.Zo)  .  j 

it.  per  day. 

(2)  Coefficient  and  Pressure  Extension  revised. 

(14.4  +  .25)* 


Q  =  24X16664  ~  V  (14.4+8)16  =  8,768,000  cu.  ft. 

per  day. 

(3)    Coefficient  not  revised,  Pressure  Extension  not  revised. 


(2  =  24X16664    V(14.4+ 10)  16  =  7,927,000  cu.  ft.  per  day. 

(4)     Coefficient  not  revised.     Pressure  Extension  revised. 
<3  =  24X16664    V (14.4+8)  16  =  7,572,000  cu.  ft.  per  day. 

Whether  method  (2)  or  (4)  should  be  applied  depends  upon 
the  contract. 


*  See  Page  189  for  revision  of  coefficient  for  change  of  atmospheric  pressure. 

228 


MEASUREMENT      OF      GAS      AND      AIR 


Fig.    86— ORIFICE,    FLANGES    AND    50    INCH    DIFFERENTIAL    GAUGE 
INSTALLATION.     PIPE   TAP  CONNECTIONS.     NOTE  BY-PASS 
BETWEEN  GAUGE  LINES 


229 


MEASUREMENT      OF      GAS      AND      AIR 

GAS  CONTRACTS 

All  true  contracts  begin  with  an  agreement.  By  agree- 
ment is  meant  the  meeting  of  the  minds  of  the  contracting 
parties  in  a  common  assent  to  the  same  definite  conclusion. 
In  order  that  the  agreement  may  cover  completely  all  points 
over  which  doubt  may  arise  it  should  be  drawn  up  as  complete 
as  possible. 

The  following  are  specimen  clauses  which  appear  in  gas 
leases  regarding  the  methods  of  measurement  of  gas: 

"All  meters  necessary  for  the  Measurement  of  Gas  under 
this  contract  shall  be  furnished  by  the  buyer  and  shall  be 

either or at  the  option  of  the  buyer 

and  gas  measurement  by  same  shall  be  corrected  to  a  basis 

of oz.  pressure.  It  is  agreed  that  should  the  meter, 

for  any  reason,  fail  to  work  and  fail  to  register  the  amount  of 
gas  to  the  buyer,  then  the  amount  to  be  paid  by  the  buyer 
during  such  time  as  the  meters  shall  fail  to  register,  shall  be 
the  average  per  day  for  the  last  preceding  calendar  month 
for  which  an  accurate  meter  reading  was  had,  multiplied  by 
the  number  of  days  during  which  the  meter  failed  to  register. 
In  case  any  question  arises  as  to  the  accuracy  of  the  meter 
measurement  at  any  time,  the  meter  shall  be  tested  by  either 
party,  and  the  party  demanding  the  test  shall  pay  the  ex- 
pense of  such  test.  No  corrections  for  meter  measurements 
are  to  be  made  dating  back  to  the  last  test  prior  to  date  of 
complaint." 

"The  buyer  shall  at  his  own  expense  install  and  keep  in 

repair meters  of  standard  type  sufficient  in  size  to 

measure  the  number  of  cubic  feet  of  gas  received  by  him  under 
this  agreement,  together  with  said  meters  to  be  installed  on 
the  above  described  property.  The  said  meters  shall  be 
read  daily  in  accordance  with  rules,  methods  and  instructions 
of  the  Metric  Metal  Works  or  other  standard  forms  for 
correct  reading  of  such  meters  and  the  amount  of  gas  so 
metered  shall  be  computed  on  the  basis  of ounces  to 

230 


MEASUREMENT      OF      GAS      AND      AIR 

a  square  inch  above  atmosphere.  The  seller  shall  have  at 
all  times,  the  right  to  inspect  such  meters  providing,  however, 
the  buyer  shall  be  notified  in  time  to  be  present  when  such 
test  is  made,  if  he  so  desires.  And  it  is  agreed  that  if,  after 
such  examination  it  shall  be  found  that  the  meter  or  meters 
are  correctly  measuring  or  registering  the  said  gas,  then  the 
expense  of  such  examination  and  test  shall  be  borne  by  the 
seller,  but  if  it  shall  be  found,  after  such  examination,  that 
the  said  meter  or  meters  are  in  bad  repair,  or  do  not  correctly 
measure  or  register  the  gas,  then  the  party  of  the  second  part 
shall  correct  same  at  his  own  expense  and  pay  expense  of 
such  examination." 

Other  contracts  have  been  prepared  which  read  as  follows : 

"The  meters  to  be  used  in  the  Measurement  of  Gas  shall 
be  Orifice  Meters  and  furnished  by  the  buyer,  and  the  amount 

of  gas  measured  shall  be  reduced  by  calculations  to oz. 

pressure  above  an  assumed  atmospheric  pressure  of  14.4  and 
the  volume  shall  be  expressed  at  a  temperature  of  60  deg. 
fahr." 

Inasmuch  as  a  contract  is  legally  assumed  to  be  a  meeting 
of  the  minds  of  the  parties  making  the  contract,  it  is  very 
essential  that  the  contract  shall  contain  sufficient  data  or 
description  to  eliminate  a  different  interpretation  or  con- 
struction being  placed  upon  the  words  by  either  of  the  parties. 

On  Pages  221  to  228  the  subject  of  atmospheric  pressure  is 
explained  in  detail,  and  on  Page  171  the  minor  deviations 
due  to  standard  values  used  in  the  computation  of  formulas 
etc.,  are  mentioned.  In  order  that  the  parties  of  the  contract 
shall  have  full  knowledge  of  the  basis  of  measurement,  it  is 
recommended  that  the  subject  of  the  Table  of  Hourly  Orifice 
Coefficients  to  be  used  should  be  incorporated  as  well  as  a 
more  definite  phraseology  regarding  pressure  base  on  which 
the  gas  shall  be  calculated,  especially  in  those  fields  where 
the  average  atmospheric  pressure  varies  appreciably  below, 
or  above  14.4  Ib.  per  square  inch. 

231 


MEASUREMENT      OF      GAS      AND      AIR 

On  Pages  221  to  228  it  is  noted  that  the  difference  of  at- 
mospheric pressure  produces  a  considerable  effect  upon  the 
basis  of  measurement  or  upon  the  value  of  the  coefficient 
used  when  different  interpretations  are  placed  upon  the  term 
"atmospheric  pressure."  In  order  that  the  same  quantity 
of  gas  shall  constitute  a  cubic  foot  as  far  as  is  practically 
possible,  (which  would  exactly  constitute  the  same  cubic 
foot  at  all  places)  the  use  of  absolute  atmospheric  pressure  is 
recommended,  an  expression  of  a  certain  number  of  ounces 
above  an  assumed  atmospheric  pressure  of  14.4.  A  cubic 
foot  of  gas  at  10  oz.  above  the  assumed  atmospheric  pressure 
of  14.4  or  an  absolute  pressure  of  15.025  pounds  would  con- 
tain exactly  the  same  weight  of  gas  at  any  place  providing 
the  chemical  constituents  of  the  gas  were  the  same. 

The  Bureau  of  Mines  has  issued  definite  instruction  in 
regard  to  pressure  base  and  temperature  base  as  follows. 

ARTICLE  15*  REVISED  MAY  31,  1921. 

"All  gas  subject  to  royalty  shall  be  measured  by  meters 
approved  by  the  supervisor  and  installed  at  the  expense  of 
the  lessee  at  such  places  as  may  be  determined  by  the  super- 
visor or  his  deputy.  The  standard  of  pressure  in  all  measure- 
ments of  gas  sold  or  subject  to  royalty  shall  be  10  ounces 
above  an  atmospheric  pressure  of  14.4  pounds  per  square  inch 
regardless  of  the  atmospheric  pressure  at  the  point  of  meas- 
urement, and  the  standard  of  temperature  shall  be  60  deg. 
fahr.  and  all  measurements  of  gas  shall  be  reduced  by  com- 
putation to  these  standards  no  matter  what  may  have  been 
the  pressure  and  temperature  at  which  the  gas  was  actually 
measured." 

It  is  noted  on  Page  224  that  if  this  is  the  intention  of  the 
party  entering  the  agreement  to  use  a  base  above  an  assumed 
pressure  of  14.4  lb.,  no  revision  is  required  for  the  Coefficients. 

*  Plan  for  Conducting  Work  under  Operating  Regulations  to  Govern  the  Pro- 
duction of  Oil  and  Gas.  Under  the  Act  of  February  25,  1920. 

232 


MEASUREMENT      OF      GAS      AND      AIR 

During  the  past  few  years  some  companies  have  made 
their  own  orifice  discs  or  have  had  them  made  at  a  nearby 
machine  shop  and  have  calculated  Coefficients  for  the  discs 
from  data  given  in  books  of  reference.  In  addition,  many 
companies  have  prepared  tables  of  Orifice  Coefficients  based 
upon  an  average  mean  curve  of  values  of  the  "coefficient  of 
velocity"  which  Coefficients  deviate  from  those  which  have 
been  published  by  the  various  manufacturers.  For  example, 
the  Tables  of  Coefficients  for  2J/2  diameters  upstream  and  8 
diameters  downstream,  as  published  in  this  book,  were  com- 
puted from  a  mean  curve  drawn  through  the  plotted  values 
of  the  coefficient  of  velocity  as  determined  by  experiment. 
This  curve  was  plotted  on  a  very  large  scale  and  the  values 
of  the  coefficient  of  velocity  were  obtained  from  the  curve 
by  inspection.  After  several  years  work  a  formula  was  de- 
rived for  a  curve  by  using  four  points  on  the  plotted  curve, 
which  very  closely  approximated  the  original  curve.  However, 
in  some  places  the  curve  of  the  formula  deviates  from  the 
plotted  curve  by  approximately  one-tenth  of  one  per  cent  and 
therefore  any  Coefficients  obtained  by  use  of  the  formula 
will  differ  by  one-tenth  of  one  per  cent  from  the  Coefficients 
derived  from  the  plotted  curve.  Even  though  the  matter 
of  even  one-quarter  of  a  per  cent  has  no  appreciable  effect 
upon  the  price  per  thousand  cubic  feet  of  gas  in  preparing 
the  contract,  the  mention  of  a  certain  published  Table  of 
Coefficients  or  a  statement  of  the  Coefficients  to  be  used, 
incorporated  as  a  part  of  the  contract  would  eliminate  the  dis- 
cussion or  friction  between  the  chart  reading  departments  of 
the  parties  to  the  contract.  It  is  obvious  that,  if  one  party 
was  using  a  Table  in  which  the  Hourly  Orifice  Coefficient  for 
a  4  x  2  orifice  at  4  oz.  pressure  base,  atmospheric  pressure  14.4, 
base  and  flowing  temperature  60  deg.  fahr.,  specific  gravity  .6, 
was  2,019.4  and  the  other  party  used  a  Table  where  the  Co- 
efficient for  the  same  orifice  under  the  same  conditions  was 
2,014.0  that  there  would  be  a  difference  at  the  rate  of  five 

233 


MEASUREMENT      OF      GAS      AND      AIR 


234 


MEASUREMENT      OF      GAS      AND      AIR 

dollars  for  each  $2000  worth  of  gas  sold.  It  is  also  perfectly 
obvious  that  if  the  gas  is  being  sold  at  40  cents  per  thousand, 
the  acceptance  or  rejection  of  the  contract  would  never 
hinge  on  whether  the  rate  should  be  40  or  40.1  cents  per 
thousand.  However,  after  contracts  have  been  made  these 
variations  in  tables  have  been  brought  up  by  parties  interested 
with  consequent  friction.  The  incorporation  of  either  a  ref- 
erence to  the  Table  to  be  used  or  the  publication  of  a  Table 
as  a  part  of  the  contract  wrould  eliminate  most  of  the  friction 
which  now  exists  relative  to  the  use  of  Coefficients  and 
methods  of  determination  of  volumes. 

A  clause  of  which  the  following  is  an  example  could  be  used. 

"All  meters  necessary  for  measurement  of  gas  under  this 

contract  shall  be  furnished  by  the  buyer  and  shall  be 

orifice  meters.  The  gas  measurement  determined  by  same 
shall  be  revised  to  a  pressure  base  of  8  oz.  above  an  assumed 
atmospheric  pressure  of  14.4  Ib.  per  square  inch  (absolute 
pressure  14.9  Ib.  per  square  inch).  The  basis  of  temperature 
for  measurement  shall  be  60  deg.  fahr.  The  values  of  the 
Coefficients  used  for  orifices  shall  be  those  contained  on  Page 
...  of  the  book  "Measurement  of  Gases  and  Liquids  by 
Orifice  Meter,"  published  by  the  Metric  Metal  Works.  The 
Coefficient  shall  be  revised  for  changes  in  specific  gravity  of 
gas  using  multipliers  in  Table  ...  in  book  above  referred  to. 

The  specific  gravity  shall  be  determined  by  the 

method  monthly  or  about  the  25th  of  the  month.  Repre- 
sentatives of  both  parties  shall  be  present  at  the  test  and 
their  decision  shall  be  the  basis  for  calculation  for  the  fol- 
lowing month .revision  to  the  Coefficient  used 

shall  be  made  on  account  of  flowing  temperature.  The 
average  temperature  for  each  week  shall  be  obtained  by  a 
recording  thermometer.  In  case  that  there  is  no  revision  to 
the  coefficient  the  word  "no"  is  inserted  and  the  second 
sentence  relative  to  method  obtaining  temperature  is 
omitted. 

235 


MEASUREMENT      OF      GAS      AND      AIR 

In  the  example  given  above  the  reference  to  this  Hand 
Book  may  be  replaced  by  reference  to  other  published  tables, 
or  tables  prepared  and  made  a  part  of  a  contract. 

An  additional  phrase  in  regard  to  Coefficients  for  various 
sizes  of  orifices  not  given  in  the  above  Tables,  follows: 
Coefficients  for  orifices  not  given  in  the  above  Table  shall  be 
calculated  from  the  formulae  given  on  Page  .  .  .  from  the 
book  "Measurement  of  Gases  and  Liquids  by  Orifice  Meter," 
and  such  values  shall  be  used  only  after  agreement  by  both 
parties. 

MULTIPLE  ORIFICE  METER  INSTALLATION 

In  cases  where  the  flow  of  gas  varies  over  very  wide 
limits  it  may  become  necessary  to  install  meters  on  parallel 
lines  to  accurately  measure  the  minimum  rate  of  flow. 

Fig.  88  shows  a  layout  for  this  purpose.  When  the  rate 
of  flow  is  small,  the  Regulator  or  Differential  Gas  Relief 
Valve  prevents  the  gas  from  flowing  through  the  secondary 
meter  and  thus  all  of  the  gas  passes  through  and  is  measured 
by  the  primary  meter.  As  the  rate  of  flow  through  the 
primary  meter  increases,  the  differential  pressure  increases. 
When  the  differential  pressure  reaches  a  certain  pre-deter- 
mined  amount  which  is  slightly  less  than  the  maximum 
range  of  the  primary  differential  gauge,  the  differential  pres- 
sure which  also  acts  on  the  regulator,  causes  the  regulator 
to  open  the  valve  quickly  and  permit  the  increased  quantity 
of  gas  to  flow  through  both  lines  and  be  measured  by  two 
meters,  both  meters  being  in  operation  when  larger  quantities 
of  gas  are  flowing.  When  the  gas  volume  decreases  the 
differential  pressure  at  each  orifice  meter  decreases  and  when 
it  has  reached  a  certain  minimum  which  is  insufficient  to 
create  a  fair  differential  reading  on  both  of  the  charts  the 
Differential  Relief  Valve  closes  and  causes  all  of  the  gas  to 
pass  through  the  primary  meter, 

236 


MEASUREMENT      OF      GAS      AND      AIR 


8 


237 


MEASUREMENT      OF      GAS      AND      AIR 


Fig.  89 


238 


MEASUREMENT      OF      GAS      AND      AIR 


INSTALLING  GAS  OR  AIR  METERS 

The  location  of  taps  in  the  main  line,  for  pressure  con- 
nections between  the  pipe  line  and  the  Differential  Gauge 
are  dependent  upon  the  Hourly  Orifice  Coefficients  which 
are  used,  and  vice  versa. 

Connections  2^  diameters  upstream  and  8  diameters 
downstream  from  the  orifice  are  Full  Flow  Connections.  The 
stream  flow  occupies  the  full  section  of  the  pipe  at  the  taps 
and  is  not  restricted  in  area  which  is  the  case  for  all  points 
closer  to  the  orifice.  See  Fig.  90.  Flange  Connections 
are  also  used  for  gas,  air,  and  water  measurement. 


MM- 


Orifice/ 

Fig.  90— FULL  FLOW  CONNECTIONS        Fig.  91— FLANGE  CONNECTIONS 

SKETCHES  OF  ORIFICE   METER  INSTALLATIONS.          CURVED 
LINES  ARE  LINES  OF  STREAM  FLOW 

When  Full  Flow  Connections  are  used  as  in  Fig.  90,  the 
static  pressure  recorded  at  G  is  the  pressure  at  U.  For 
Flange  Connections  the  line  pressure  at  D  is  recorded  on  the 
chart,  See  Fig.  91. 

When  Gauges  are  received  with  the  Static  Pressure 
Spring  connected  with  the  upstream  pressure  portion  of  the 
Differential  Gauge,  no  change  is  required  when  used  with  Full 
Flow  Connections.  However,  when  Flange  Connections  are 
used  the  Static  Pressure  Spring  must  be  connected  to  the 
downstream  portion  of  the  Differential  Gauge.  In  this 
case  remove  the  stuffing  box  at  M  (at  the  end  of  the 
flexible  steel  tubing)  from  the  high  pressure  side  of  the  gauge 
and  attach  it  to  the  low  pressure  portion  at  tap  F.  The 
tubing  is  flexible  and  may  be  bent  in  any  position. 

239 


MEASUREMENT       OF      GAS      AND      AIR 


240 


MEASUREMENT      OF      GAS      AND      AIR 

Orifice  Meter  Installation  For  Measuring  Gases 

Install  the  meter  as  far  as  possible  from  compressors, 
pumps  or  regulators.  It  is  impossible  to  accurately  measure 
any  gas  or  liquid  subject  to  violent  pulsation. 

The  installation  should  be  made  with  a  level  section  of 
pipe  on  each  side  of  the  orifice,  using  a  straight  run  of  pipe 
of  the  same  diameter  without  any  fittings  of  any  description 
within  a  distance  of  16  diameters  of  pipe  in  either  direction 
from  the  orifice. 

When  installing  in  a  gas  line  place  one  gate  valve  at  a 
distance  of  16  diameters  or  greater  upstream  from  the  orifice 
and  another  gate  valve  at  the  same  distance  downstream. 
Gas  must  be  dry  to  obtain  proper  measurement.  Use 
drips  at  all  low  points  in  the  line  to  remove  condensates. 


Fig.  93— AN  INSTALLATION   USED  IN   THE  OS  AGE  INDIAN 
RESERVATION.     SEE  PAGE  164 


The  minimum  distances  of  16  diameters  mentioned, 
apply  for  all  locations  where  it  is  possible  to  obtain  this  dis- 
tance on  each  side  of  the  orifice  without  any  valves  or  elbows. 
Distances  less  than  these  have  been  used  satisfactorily  and 
it  is  quite  possible  to  reduce  this  distance,  although  no  de- 
finite rule  can  be  given  as  to  the  effect  that  different  com- 
binations of  fittings  at  each  location  will  produce. 

It  is  possible  to  test  out  orifice  installations  in  which 
shorter  lengths  of  straight  pipe  have  been  used  on  each  side 

241 


MEASUREMENT      OF      GAS      AND      AIR 

of  the  orifice.  This  is  accomplished  by  drilling  3  one-quarter 
inch  holes  in  the  pipe  at  2J^  diameters  upstream,  one  hole  in 
the  top  of  the  pipe  and  one  on  each  side  of  the  pipe  where 
the  upstream  section  is  less  than  16  diameters  in  length.  In 
case  the  downstream  section  is  less  than  16  diameters  in 
length,  the  three  holes  should  be  drilled  at  8  diameters  from 
the  orifice,  one  on  top  and  one  on  each  side  of  the  pipe.  If 
the  stream  line  flow  through  the  orifice  converges  and  di- 
verges uniformly,  the  pressure  at  any  two  of  the  three  taps 
upstream  or  downstream  should  be  the  same.  If  there  is 
any  appreciable  difference  in  the  pressures  at  either  set  of 
taps  it  is  evident  that  the  stream  line  flow  is  not  concentric 
with  the  pipe.  In  order  to  make  a  simple  test,  connect  one 
column  of  a  U  tube  to  the  tap  in  top  of  the  pipe,  and  the  other 
column  to  one  of  the  taps  in  the  side  of  the  pipe.  When  the 
normal  rate  of  flow  exists  through  the  orifice,  the  difference 
in  the  heads  of  the  water  in  the  two  columns  of  the  U  tube 
should  not  be  more  than  one-quarter  of  an  inch.  If  more 
than  this,  it  is  evident  that  the  flow  of  the  gas  is  influenced 
by  some  condition  other  than  the  orifice. 

The  stream  line  flow  through  the  orifice  will  be  the 
same  irrespective  of  where  the  pressure  taps  are  made.  It 
does  not  make  any  difference  whether  they  are  made  at  the 
pipe  connections,  at  the  flanges  or  at  other  intermediate 
points.  Any  condition  which  will  affect  the  stream  line 
flow  other  than  the  orifice  will  affect  the  differential  readings. 

A  by-pass  for  the  main  line  should  be  installed,  connecting 
the  main  line  ahead  of  the  inlet  valve  and  the  main  line 
beyond  the  outlet  valve,  around  the  meter  layout. 

The  size  of  pipe  for  the  by-pass  should  be  one  half  of  the 
diameter  of  the  main  or  greater  and  contain  one  valve,  or 
two  valves  with  a  sleeve  between  them.  In  the  latter  case 
when  the  valves  are  closed  the  sleeve  can  be  left  open  and 
thus  prevent  the  flow  of  any  gas  through  the  by-pass. 

242 


MEASUREMENT      OF      GAS      AND      AIR 


243 


MEASUREMENT      OF      GAS      AND      AIR 


214 


MEASUREMENT      OF      GAS      AND      AIR 

Orifice  Meter  Body 

Set  the  meter  level  in  the  line  with  the  inlet  and  outlet 
lines  connected  to  the  correct  end  of  the  meter  casting. 

Leave  space  under  the  body  so  that  the  drain  plug  can  be 
removed  whenever  desired. 

Use  oil  on  the  thread  of  the  orifice  disc  before  screwing 
into  place.  Screw  disc  tight  but  without  using  force. 

Orifice  Meter  Flanges 

Set  up  the  Flanges  so  that  the  jack  screws  are  level 
with  each  other.  Flanges  tapped  for  pressure  connections 
should  be  set  with  the  taps  vertical. 

Place  orifice  disc  with  bevelled  edge  downstream. 

Use  a  gasket  on  each  side  of  the  orifice  disc.  These 
gaskets  should  contain  openings  as  large  as  the  pipe  and 
should  be  shellaced  on  the  pipe  flanges.  Do  not  use  shellac 
on  the  face  of  the  gaskets  next  to  the  orifice  plate,  white 
lead  is  preferable. 

Gauge  Line  Connections  or  Taps  For  Full  Flow 
or  Pipe   Connections 

(2}/2  Diameters  Upstream  and  8  Diameters  Downstream) . 

See  Pages  251  to  254. 

Tap  the  pipe  line  at  U,  2J/£  diameters  upstream,  and  at  D 
8  diameters  downstream  from  the  orifice  for  J^  inch  pipe 
connections  to  the  differential  gauge.  Larger  connections 
may  be  used. 

Tap  above  the  center  of  the  pipe,  so  that  any  condensate 
accumulating  in  the  connections  will  drain  into  the  main. 

The  openings  must  be  tapped  clean  and  perpendicular 
to  the  pipe  line.  After  the  nipples  have  been  screwed  in, 
examine  the  interior  of  the  pipe  to  be  sure  that  there  are  no 
burrs  or  that  the  nipple  does  not  extend  into  the  pipe.  All 
burrs,  chips,  etc.,  should  be  removed.  The  inside  of  the  pipe 
should  have  a  smooth  surface  at  the  tap,  otherwise  the  dif- 
ferential reading  may  be  affected. 

245 


MEASUREMENT      OF      GAS      AND      AIR 

Instead  of  making  taps  in  the  pipe  line  for  the  connections 
if  possible  weld  a  short  length  of  J4  incn  pipe  to  the  main 
at  points  U  and  D  then  drill  the  pipe  with  a  small  drill  pass- 
ing through  the  nipple.  This  will  avoid  the  possibility  of 
any  large  projections  in  the  pipe. 

Taps  1}/2  diameters  upstream  and  8  diameters  downstream 
from  the  face  of  the  orifice,  are  10  inches  upstream  and  32 
inches  downstream  for  a  4  inch  pipe. 

Screw  two  J4  inch  pipe  plugs  in  taps  in  flanges,  if  flanges 
contain  taps. 

Gauge    Line    Connections    or    Taps 

For  Flange  Connections 
See  Pages  252  to  254. 

Flanges  furnished  for  Orifice  Meters  contain  holes 
tapped  for  }^  inch  pipe. 

Hourly  Orifice  Coefficients  for  Flange  Connections  are 
not  the  same  as  for  Full  Flow  Connections  (2J^  diameters 
upstream  and  8  diameters  downstream). 

Orifice  Meter  for  Coke  Oven  Gas 

In  an  installation  for  measuring  Coke  Oven  Gas,  place 
the  orifice  disc  (with  the  small  hole  in  the  disc  below  the 
orifice)  between  Steam  Jacketed  Flanges,  so  that  the  meter 
can  be  kept  heated.  Any  tar  which  is  deposited  on  the 
orifice  plate  will  be  kept  in  a  fluid  state  and  will  run  off, 
leaving  a  thin  skim  which  will  prevent  the  orifice  plate 
from  being  oxidized  by  the  action  of  the  ammonium  sulphates 
contained  in  the  gas.  The  tar,  which  is  deposited  on  the  up- 
stream side  of  the  orifice,  is  drained,  by  the  small  opening  in 
the  orifice  plate,  into  the  downstream  side,  where  it  may  be 
drained  off  by  a  drip  placed  in  the  line.  The  tar  will  form  a 
seal  for  the  small  hole  in  the  plate.  All  other  instructions 
are  identical  with  those  for  measuring  gas. 

246 


MEASUREMENT      OF      GAS      AND      AIR 

INSTALLING  THE  RECORDING  DIFFERENTIAL  AND 
STATIC    PRESSURE    GAUGE 

For  Measuring  Gas  or  Air 

100  inch  Gauge  and  Orifice  Meter  Body.  Page  251. 
50  inch  Gauge  and  Orifice  Meter  Body.  Page  251. 
50  inch  Gauge,  Full  Flow  Connections.  Page  252. 
50  inch  Gauge,  Flange  Connections.  Page  252. 

10  inch  or  20  inch  Gauge,  Full  Flow  Connections.  Page  253. 
10  inch  or  20  inch  Gauge,  Flange  Connections.     Page  253. 
50  inch  or  100  inch  Gauge,  Full  Flow  Connections.  Page  254. 
50  inch  or  100  inch  Gauge,  Flange  Connections.     Page  254. 
These  instructions  apply  to  any  of  the  diagrams  above 
mentioned.     See  Pages  251  to  254. 

Setting  up  Gauge — Install  the  gauge  on  a  2  inch 
pipe  support,  attached  to  the  line  or  on  a  solid  foundation. 
It  may  be  attached  directly  to  a  solid  post  or  placed  on  a 
shelf.  The  gauge  must  be  set  level  and  rigid  so  that  it  will 
not  be  affected  by  any  excessive  vibration. 

Differential  Pen  Arm — Remove  the  plate  (on  which 
the  number  plate  is  fastened)  and  attach  the  differential  pen 
arm  in  accordance  with  the  instructions  pasted  on  face  of 
chart. 

Glass — Remove  the  glass  face  from  box  of  charts  and 
attach  to  frame  underneath  the  wire  clips. 

Adding  Mercury — Remove  the  plug  with  rod  from 
the  funnel  in  the  top  casting  and  pour  in  the  mercury, 
which  is  shipped  in  a  pipe  container.  The  plug  with  the 
rod  attached  is  used  only  in  shipping  the  gauge. 

Add  mercury  until  the  differential  pen  rests  at  zero. 
The  float  should  rise  about  one-eighth  inch  above  the  bot- 
tom of  the  low  pressure  chamber.  When  the  pen  rests 
at  zero  insert  a  small  rod  through  the  funnel  opening, 
touch  the  float  and  be  sure  that  it  is  floating  and  not  resting 
on  the  bottom  of  the  chamber.  The  funnel  is  closed  with 
the  one-eighth  inch  plug  shipped  with  the  gauge. 

247 


MEASUREMENT      OF      GAS      AND      AIR 

Static  Pressure  Connections — On  account  of  the  vari- 
able conditions  under  which  meters  and  gauges  are  in- 
stalled, it  is  impossible  to  present  layouts  which  will  meet  all 
requirements.  However,  the  instructions  and  layouts  in- 
dicating the  relative  location  of  test  connections  V  and  P, 
and  valves  should  be  strictly  followed. 

Connect  the  tap  in  gauge  at  H  with  the  tap  U  in  the  line, 
and  tap  L  in  the  gauge  with  tap  D  in  the  line,  with  %  inch 
pipe.  Larger  pipe  and  fittings  may  be  used. 

Insert  valves  in  the  connecting  lines  just  above  the  taps 
in  the  main  with  unions  above  the  valves. 

Drips  may  be  installed  in  gauge  lines  for  the  purpose 
of  collecting  moisture  and  acting  as  partial  shock  absorbers. 
They  are  generally  omitted. 

Always  give  the  lines  a  slight  slant  from  the  gauge  toward 
the  main  and  avoid  any  traps.  Place  valves  and  fittings 
in  the  same  relation  to  each  other  as  shown  in  diagram. 

Supplementary  valves  W  and  X  may  be  placed  near  the 
gauge  if  the  gauge  is  located  some  distance  from  the  line. 
Place  them  between  the  pipe  line  taps  U  and  D,  and  the  test 
or  by-pass  connections,  never  between  the  gauge  and  any 
test  or  by-pass  connection. 

By-Pass — It  is  desirable  to  install  a  by-pass  as  shown, 
placing  valves  at  Y  and  Z  and  plug  or  valve  at  K. 

Removing  Chart — To  remove  the  chart,  raise  the 
pens  from  chart  with  the  pen  lifter  and  remove  the  knurled 
thumb-nut  in  the  center.  The  metallic  dial  can  be  taken 
off  by  twisting  it  slightly  to  the  left  after  the  four  holding 
screws  have  been  loosened.  (Do  not  take  them  out). 

Clock — The  clock  should  be  wound  with  the  key 
furnished  with  the  instrument.  The  movement  is  carefully 
timed  before  leaving  the  factory;  however,  if  it  should  be 
necessary  to  regulate  it,  remove  the  dial  and  cover  of  clock 
box,  and  shift  the  small  regulating  lever  in  the  proper  di- 
rection. Clock  movements  are  usually  wound  each  day  but 
will  run  for  two  days. 

248 


MEASUREMENT      OF      GAS      AND      AIR 

Placing  Chart — Keep  the  pens  from  resting  on  dial 
by  means  of  pen  lifter  and  slip  on  a  chart  without  touching 
the  pens.  Set  the  chart  so  that  the  pens  will  point  to  the 
particular  hour  of  the  day  desired  and  secure  in  place  with 
the  knurled  thumb-nut. 

Pens  and  Ink — Fill  the  V  shaped  pens  with  ink 
using  the  ink  dropper.  Do  not  fill  the  pen  more  than  two- 
thirds  full  and  see  that  the  ink  flows  when  the  pen  touches 
the  chart.  Use  black*  ink  in  the  lower  or  static  pressure 
marking  pen  and  red  ink  in  the  upper  or  differential  pressure 
marking  pen.  Use  the  special  ink  only.  Clean  the  pens 
frequently  using  a  moistened  edge  or  piece  of  blotting  paper. 
To  protect  the  pens  the  chart  should  be  kept  on  the  instru- 
ment whether  in  operation  or  not.  Pens  should  rest  at  zero 
before  turning  gas  or  air  into  the  meter  and  gauge.  Be 
sure  that  the  pen  bears  lightly  on  the  chart,  enough  to  make 
a  clear  line,  but  not  so  hard  as  to  impair  its  sensitiveness. 
Do  not  bend  the  pens  up  or  down  but  let  them  incline 
as  received  if  they  follow  the  arc.  The  ink  will  rise,  due  to 
capillary  attraction. 

Turning  on  Gas  or  Air. 
Close  K 
Open  Y  and  Z 
Then  open  W  and  X 

After  the  pressure  is  equalized  in  both  portions  of  the  gauge 
Close  Y  and  Z 
OpenK 

Leaks — Be  sure  that  valves  Y  and  Z  do  not  leak. 
Test  all  connections  with  soap  suds  and  stop  all  leaks.  Look 
after  valve  stems  especially. 

Orifice  Capacity — After  gauge  is  in  operation,  if  the 
differential  pen  records  near  the  maximum  reading,  change 
the  orifice  for  one  of  a  larger  size.  If  this  is  not  possible 
and  it  is  found  that  the  flow  of  gas  keeps  the  marking  arm 

*  Blue  or  green  ink  may  be  used. 

249 


MEASUREMENT      OF      GAS      AND      AIR 

at  or  above  the  maximum  differential  circle,  it  will  be  neces- 
sary to  use  a  larger  size  of  line  and  orifice  flanges  or  meter 
casting  in  order  to  use  a  larger  size  of  orifice,  or  use  a  dif- 
ferential gauge  with  a  higher  range  of  differential. 

If,  after  twenty-four  hours,  the  differential  reading  ranges 
at  or  below  10  per  cent  of  the  maximum  range  of  the  chart 
in  inches,  change  the  orifice  for  one  of  a  smaller  size  or  use  a 
differential  gauge  with  a  smaller  maximum  range.  Tem- 
porarily the  gas  may  show  an  abnormally  high  static  and 
differential  pressure  until  the  flow  becomes  settled. 

For  tables  of  different  sizes  of  orifices  required  for  measur- 
ing gas  and  air,  see  Pages  214  to  217. 

Vibrating  Differential  Pen  Arm — The  hole  in  the  bottom 
of  the  mercury  pot  of  gauges,  Figs.  97,  98,  and  99,  is  % 
inch  in  diameter.  When  the  gas  measured  shows  a  pulsation 
which  affects  the  differential  pen  arm  marking  on  the  chart, 
decrease  the  size  of  the  opening  in  the  mercury  pot  by 
screwing  in  one  of  the  two  bushings  shipped  with  the  gauge. 
For  severe  vibration  use  the  bushing  having  a  TS  inch  hole. 
For  slight  vibration  use  the  bushing  having  a  J/g  inch  hole. 
In  testing  gauges  for  accuracy  when  a  small  hole  bushing  is 
used,  allow  extra  time  for  the  mercury  to  reach  its  level 
before  reading  chart.  The  bushing  furnished  for  the  U  type 
of  gauges  is  screwed  in  the  upper  end  of  the  J/g  incn  pipe 
where  it  enters  the  low  pressure  chamber.  In  gauges, 
Figs.  100  and  109,  the  vibration  is  lessened  by  reducing  the 
opening  in  the  rubber  gasket,  (which  is  placed  between 
the  bottom  casting  and  the  ring  forming  the  division  be- 
tween the  high  and  low  mercury  chamber),  with  a  small 
wooden  wedge. 

If  the  static  pressure  pen  arm  vibrates  regularly  and 
rapidly  install  the  meter  farther  from  the  source  of  the 
pulsation.  Never  partially  close  the  valves  W  or  X  when  in 
operation.  See  Pulsating  Flow,  Page  143. 

250 


MEASUREMENT      OF      GAS      AND      AIR 


K 


-3£j/ametcrs • 


Fig.  96— ORIFICE  METER  BODY  AND  50  OR  100  INCH  GAUGE 
INSTALLATION  FOR  MEASURING  GAS  OR  AIR 


Fig.  97— ORIFICE  METER  BODY  AND  50  INCH  GAUGE  INSTALLATION 
FOR  MEASURING  GAS  OR  AIR 

251 


MEASUREMENT      OF      GAS      AND      AIR 


—^Diameters 


,  98—50  INCH  GAUGE  INSTALLATION  FOR  MEASURING  GAS  OR 
AIR,  FULL  FLOW  CONNECTIONS 


Downstream  Connection 


Fig.  99—50  INCH  GAUGE  INSTALLATION  FOR  MEASURING  GAS  OR 
AIR,  FLANGE  CONNECTIONS 

252 


MEASUREMENT      OF      GAS      AND      AIR 


Fig.   100—10  OR  20  INCH  GAUGE  INSTALLATION  FOR  MEASURING 
GAS  OR  AIR,  FULL  FLOW  CONNECTIONS 


Upstream  Connect  tor. '//        Dty 


Fig.  101—10  OR  20  INCH  GAUGE  INSTALLATION  FOR  MEASURING 
GAS  OR  AIR,  FLANGE  CONNECTIONS 

253 


MEASUREMENT      OF      GAS      AND      AIR 


^Diameters- 


Fig.  102—50  OR  100  INCH  GAUGE   INSTALLATION  FOR  MEASURING 
GAS  OR  AIR,  FULL  FLOW  CONNECTIONS 


Drain 


Upstream  Connection 


Fig  103—50  OR  100  INCH  GAUGE   INSTALLATION  FOR  MEASURING 
GAS  OR  AIR,  FLANGE     CONNECTIONS 


254 


MEASUREMENT      OF      GAS      AND      AIR 

TESTING  DIFFERENTIAL  GAUGES 

For  Measuring  Gas  or  Air 

Gauges  should    be  checked  daily   or  weekly  by  turning 
off  the  gas  to  see  if  the  marking  arms  rest  at  zero. 
Checking  Gauge  for  Zero: — 
Close  K 
Open  Y  and  Z 
Close  W  and  X 

The  differential  pen  arm  should  return  to  zero. 
Open  K  slowly  and  allow  the  gas  or  air  to  escape  slowly 
into  the  atmosphere,  thus  making  sure  that  there  is  no  pres- 
sure on  either  portion  of  the  gauge. 

The  static  pressure  pen  arm  should  return  to  zero. 
There  will  be  a  slight  difference  between  the  zero  position 
of  the  differential  pen  arm  when  the  gauge  is  under  pressure 
and  not  under  pressure.  This  difference  is  created  by  the 
expansion  of  the  metal  under  pressure.  The  arm  should  be 
checked  for  zero  under  working  pressure  conditions.  The 
difference  between  the  zero  position  under  working  pressure 
and  not  under  pressure  should  be  noted  and  this  constant 
difference  should  be  maintained  when  checked  with  the 
test  gauge. 

The  differential  pen  arm  should  be  kept  in  practically  a 
straight  line  at  the  flexible  joint.  The  differential  pen  arm 
can  be  adjusted  to  zero  by  a  small  movement  of  the  pen  arm 
at  the  flexible  joint,  or  at  the  connection  with  the  shaft. 
When  the  pen  rests  at  zero  determine  if  the  float  is  floating 
and  not  resting  on  the  bottom  of  the  mercury  pot. 
Partially  close  Y 

Open  X  carefully  when  the  differential  pen 
should  recede  one-fourth  inch  or  more  (actual 
measurement)  below  the  zero  line.  If  the  float  rests 
on  the  zero  bottom  of  the  chamber  add  mercury. 
See  paragraph  Adding  Mercury,  Page  247. 
After  test  close  X,  open  Y. 

255 


MEASUREMENT      OF      GAS      AND      AIR 

Checking  Differential  Gauge  on  Pressure  Lines — • 

Close  K 

Open  Y  and  Z 

Close  W  and  X 

OpenK 

Remove  plugs  at  P  and  V 

Attach  test  gauge  by  suitable  connections  at  P 

Close  Y,    Be  sure  Z  is  open 

Open  valve  W  slightly  when  a  pressure  will 
be  exerted  on  mercury  in  the  high  pressure  por- 
tion of  the  gauge,  and  on  the  test  gauge. 

By  partially  opening  or  closing  valve  Z,  the 
pen  arm  can  be  stopped  at  any  point  on  the  chart 
and  checked  with  the  reading  on  the  test  gauge. 

After  tests  remove  the  test  gauge  and  replace 
plugs  P  and  V. 

Proceed  as  for  Turning  on  Gas,  Page  249.. 

Checking  Differential  Gauge  on  Vacuum  Lines — 

Close  K 

Open  Y  and  Z 

Close  W  and  X 

OpenK 

Remove  plugs  V  and  P 

Attach  test  gauge  by  suitable  connections  at  V 

Close  Z 

Be  sure  Y  is  open 

Open  valve  X  slightly,  when  a  vacuum  will  be 
formed  in  the  low  pressure  portion  of  the  gauge 
also  on  the  test  gauge. 

By  partially  opening  and  closing  valve  Y  the 
pen  can  be  stopped  at  any  point  desired  and 
reading  checked  with  the  test  gauge. 

After  tests  remove  the  test  gauge  and  replace 
plugs  P  and  V. 

Proceed  as  for  Turning  on  Gas,  Page  249. 

256 


MEASUREMENT      OF      GAS      AND      AIR 


257 


MEASUREMENT      OF      GAS      AND      AIR 


Checking  Differential  Gauge  under  Working  Pres- 
sure —  If  the  glass  tubes  of  the  test  gauge  are  of  sufficient 
strength  to  hold  the  pressure,  and  the  scale  is  of  equal  range 
with  the  chart  in  inches  of  water,  the  recording  differential 
gauge  may  be  checked  with  a  test  gauge  by  connecting  one 
column  of  test  gauge  with  tap  at  P  and  the  other  column  with 
the  tap  at  V. 

Close  K 
Open  Y  and  Z 
Then  open  W  and  X 

By  partially  opening  and  closing  valve  Y  the 
reading  can  be  checked  with  the  test  gauge.  It 
can  be  left  as  a  permanent  installation  for  check- 
ing the  recorded  differential  reading  of  the  pen. 

Adjustment  —  If  the  zero  position  of  the  differential 
pen  is  O.  K.  and  the  higher  readings  of  the  differential 
pen  on  the  chart  do  not  check  with  the  test  gauge,  make  ad- 
justment by  increasing  the  length  of  the  float  lever  arm  when 
the  reading  is  fast,  and  decreasing  when  slow.  This  is  ac- 
complished by  moving  the  lock  nuts  NN  (shown  in  Figs.  105 
and  106)  in  the  proper  direction. 


Beor/ng  Shaft 


Fig.  105. 


Fig.   106. 


Testing  Static  Spring — To  test  static  spring  attach  the 
test  gauge  at  G  and  check  the  two  gauges.  The  use  of  an 
inspector's  test  gauge  is  recommended  rather  than  the  use  of 
a  portable  dead  weight  tester.  The  inspector's  test  gauge 

258 


MEASUREMENT      OF      GAS      AND      AIR 


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259 


MEASUREMENT      OF      GAS      AND      AIR 

should  be  accurately  calibrated  against  a  mercury  column  at 
proper  intervals  to  be  sure  that  it  is  accurate  and  that 
the  spring  has  not  lost  its  elasticity.  Dead  weight  testers 
under  ideal  conditions  give  satisfactory  results  but  it  is 
very  difficult  to  obtain  these  conditions  especially  in  the 
field. 

General — Before  turning  the  gas  into  the  gauge  al- 
ways be  sure  that  valves  Y  and  Z  are  open  before  opening 
valves  W  and  X  or  either  valve  W  or  X.  This  precaution 
will  eliminate  practically  all  damage  to  differential  pen  arm . 


Fig.  108 


260 


MEASUREMENT      OF      GAS      AND      AIR 

READING  CHARTS 

The  formula  for  use  in  measuring  gas  or  air  with  the  ori- 
fice meter  is 

Quantity  =  C V  hX(A±p). 

C  =  Coefficient  obtained  from  Table  of  Coefficients 
or  calculated  for  the  proper  size  of  orifice, 
diameter  of  pipe,   Pressure  Base,   Base  and 
Flowing  Temperature,  and  Specific  Gravity. 
h  =  differential  pressure  in  inches  of  water. 
A  =  atmospheric  pressure  in  Ib.  per  square  inch. 
p Astatic  pressure  expressed  in  Ib.  per  square  inch, 
plus  when  above  atmospheric  pressure,  minus 
when  below  atmospheric  pressure.     The  gauge 
pressure  above  atmosphere  is  usually  expressed 
in  pounds  per  square  inch  so  that  no  change  of 
units  is  required.     However,  vacuum  is  in- 
dicated in  inches  of  mercury  vacuum  below 
atmospheric  pressure.     To  use  this  value  in 
the  formula  it  must  be  converted  into  pounds 
per  square  inch  below  atmospheric  pressure. 
The    vacuum    in    pounds    per    square  inch, 
below  atmospheric  pressure,  is  equal   to   the 
vacuum  gauge  reading  in  inches   of    mercury 
multiplied  by  0.4908;  for 'example,  20  inches 
mercury  vacuum  is  equal  to  9.82  Ib.  per  sq.  in. 
below  atmospheric  pressure  (20  X  .4908  =  9.82) . 
To  simplify  all  calculations,  Tables  of  Pressure  Exten- 
sions have  been  published  which  give  the  results  of  the  form- 
ula   V  AX(14.4±^),  in  figures  for  various  combinations  of 
pressure  and  differential  readings  from  29  inches  vacuum  to 
500  Ib.  pressure  and  from  1  inch  to  100  inches  differential. 
This  eliminates  the  necessity  of  figuring  out  the  formula  for 
each  reading  in  determining  the  volume  of  gas  passing  the 
meter.     In   this  formula,   the   atmospheric  pressure  is   as- 
sumed as  14.4  Ib.     If  the  atmospheric  pressure  varies  ap- 

261 


MEASUREMENT      OF      GAS      AND      AIR 


Check  Valve 


Down  stir  earn  Static  Pressure  Connection 


Tap  for  Downstream 
Static  Pressure  Connection 


Mercury. 


'ream  Sta6/c  Pressure  Connection 

Tap  for  Upstream  Static  Pressure 
Connect/on 


High  Pressure  Mercury  Chamber      / 


Check 'ft, V/e 


Low  Pressure  Mercury  Chamber 
Static  Pen  firm 


Chart 


Fig.  109—10  INCH  DIFFERENTIAL  GAUGE.     SECTIONAL  VIEW 


262 


MEASUREMENT      OF      GAS      AND      AIR 

preciably  from  14.4  lb.,  adjustment  must  be  made  to  the 
static  pen  arm,  or  to  the  static  pressure  readings  as  explained 
on  Pages  221  to  228. 

To  obtain  the  quantity  passing  the  meter,  average  the 
differential  pressure  (marked  in  red  ink)  and  the  static 
pressure  (marked  in  black  ink*)  on  the  chart  for  each  hour. 
Obtain  from  the  book  of  Pressure  Extensions  the  extensions 
for  the  (differential  and  static)  pressure  readings  for  each 
hour,  add  the  extensions  together  and  multiply  the  sum  by  the 
Hourly  Orifice  Coefficient  for  the  orifice  under  the  conditions 
being  used.  The  result  will  be  the  volume  of  gas  in  cubic 
feet  passing  the  meter  for  the  period  during  which  the  pres- 
sures were  averaged. 

If  the  differential  pressure  varies  over  wide  ranges  dur- 
ing the  hourly  period,  fifteen  minute  periods  should  be  used. 
When  fifteen  minute  periods  are  used  the  sum  of  the  exten- 
sions should  be  divided  by  four  before  multiplying  by  the 
Hourly  Orifice  Coefficient. 

On  Page  265  is  shown  an  orifice  meter  chart  report  and 
on  Page  264  is  an  extract  from  a  book  of  Pressure  Extensions 
which  apply  to  the  chart  shown  on  Page  264.  To  follow  the 
work  through  in  detail,  the  chart  when  obtained  from  the 
field,  is  examined  to  note  whether  any  extraordinary  condi- 
tions took  place  at  the  meter  during  the  period.  The  dif- 
ferential pressure  on  the  chart  is  averaged  by  inspection  for 
each  hour,  and  the  average  differential  reading  is  noted 
opposite  the  differential  record,  in  pencil  on  the  chart.  Be- 
ginning at  8  A.  M.  the  average  differential  is  20^  inches 
from  8  A.  M.  to  9  A.  M.  for  the  first  hour;  22  inches  from 
9  A.  M.  to  10  A.  M.  and  22  inches  from  10  A.  M.  to  11  A.  M., 
etc.,  the  numerical  values  being  marked  in  the  hourly 
period  opposite  the  differential  record.  The  static  pres- 
sure is  then  averaged  by  inspection  for  each  hour;  being  30 
lb.  from  8  A.  M.  to  9  A.  M.,  31  lb.  from  9  A.  M.  to  10  A.  M. 

*Blue  or  green  ink  may  be  used. 

263 


MEASUREMENT      OF      GAS      AND      AIR 


PRESSURE        EXTENSIONS 

30-39  LB. 

18.5  to  100  Inches  of  Water  Differential  Pressure 


In.  Diff. 
orH. 

18.5 
19. 
.5 


30 


29  045 
29  424 


30  535 
31.254 
31 . 956 
32.644 


31 


30  507 

30.877 

31  604 

32  314 

33  009 
33  690 


32 


33 


29  612 

30  010 
30  402 


31  550 

32  292 

33  018 
33  728 


34 


30  325 
30.721 

31  113 
31  499 


35 


36 


30  535 

30  945 

31  350 

31  749 

32  144 


34  047 
34.779 

35  496 


37 


38 


31  135 
31  553 

31  966 

32  373 

32  775 

33  172 


39 


31  431 

31  853 

32  269 


18.5 
19. 

5 
20 

5 

21 


Fig.  110— EXTRACT  OF  "PRESSURE  EXTENSIONS"  APPLYING    TO 
CHART  (Fig.  111).     (Size  Reduced  one-third) 


Fig.  Ill— ORIFICE  METER  CHART 

264 


MEASUREMENT      OF      GAS      AND      AIR 


ORIFICE  METER  CHART  REPORT 

LOCATION— Lyons  No.  6.  DATE— 3-14-22. 

Meter  No.  241  Size  4x2  Orifice  Coefficient  1184.7 


Time 

Static 
Gauge 
Pressure 

Differential 
Inches 
Water 

Extension 

8-  9  A.  M. 

30 

2oy2 

30.170 

9-10  A.  M. 

31 

22 

31.604 

10-11  A.  M. 

32 

0)/i) 

IKS 

31.950 

11-12  A.  M. 

33 

22 

32.292 

12-  1  P.  M. 

34 

23 

33.365 

1-  2  P.  M. 

35 

23 

33.  70S 

2-  3  P.  M. 

35 

23 

33.708 

3-  4  P.  M. 

37 

24 

35.123 

4-  5  P.  M. 

38 

25 

36.194 

5-  6  P.  M. 

39 

25 

36.538 

6-  7  P.  M. 

38 

25 

36.194 

7-  8  P.  M. 

an 

OO 

24 

35.463 

8-  9  P.  M. 

38 

24 

35.463 

9-10  P.  M. 

37 

24 

35.123 

10-11  P.  M. 

36 

23 

34.047 

11-12  P.  M. 

36 

23 

34.047 

12-  1  A.  M. 

35 

23 

33.708 

1-  2  A.  M. 

35 

23 

33.708 

2-  3  A.  M. 

34 

23 

33.365 

3-  4  A.  M. 

33 

22 

32.292 

4-  5  A.  M. 

n>a> 
OO 

22 

32.292 

5-  6  A.  M. 

33 

21 

31.550 

6-  7  A.  M. 

34 

22 

32.631 

7-  8  A.  M. 

35 

24 

34.433 

Total 
Coefficient 
Delivery .  . 


808.97 

1184.7 

.958,387  cu.  ft. 


Fig.  112 
265 


MEASUREMENT      OF      GAS      AND      AIR 

and  32  Ib.  from  10  A.  M.  to  11  A.  M.,  etc.  The  average 
reading  for  each  hour  being  noted  on  the  chart  in  the  hourly 
period  opposite  the  static  pressure  record.  The  extension 
obtained  from  the  Table  of  Pressure  Extensions,  may  be 
written  on  the  outer  margin  of  the  chart  as  shown  in  Fig. 
111.  In  case  they  are  compiled  on  a  report  as  on  Page  265, 
all  calculations  are  made  on  the  report  and  the  extensions 
are  added  and  multiplied  by  the  Coefficient  of  the  disc  which 
will  give  the  delivery.  In  case  the  extensions  are  written 
on  the  outer  margin  of  the  chart,  they  are  added  on  an  add- 
ing machine,  the  sum  is  noted  on  back  of  the  chart,  where 
this  sum  is  multiplied  by  the  Coefficient  giving  the  quantity 
passing  for  the  day.  Where  the  chart  only  is  used  all  data 
is  compiled  on  one  record  which  eliminates  the  use  of  other 
forms  and  the  charts  for  each  meter  can  be  assembled  in  a 
large  envelope  day  by  day  with  the  extension,  Coefficient, 
and  daily  quantity  being  noted  on  the  face  of  the  envelope  as 
is  shown  in  Fig.  114.  One  envelope  is  used  for  a  month  for 
each  meter  or  location. 

To  reduce  the  work  involved,  some  companies  average 
the  differential  reading  for  the  day  and  the  static  reading  for 
the  day.  The  pressure  extension  is  obtained  for  the  aver- 
age readings  and  is  multiplied  by  the  number  of  hours  for 
which  the  average  was  obtained.  This  product  is  then 
multiplied  by  the  Hourly  Orifice  Coefficient.  The  average 
differential  for  the  chart  shown  on  Page  264  is  23  inches. 
The  average  pressure  is  35  Ib.  The  extension  of  these 
average  values  is  33.708,  which  multiplied  by  24  equals  the 
total  of  the  pressure  extensions  for  the  day.  (24X33.708  = 
808.99).  It  will  be  noted  that  this  result  is  slightly  greater 
than  that  derived  by  obtaining  the  extension  for  each  hour 
and  adding.  Where  the  differential  and  static  pressure 
records  do  not  vary  over  wide  ranges  this  method  will  give 
results  which  will  check  very  closely  with  the  previous  meth- 
od. However,  these  results  will  invariably  be  higher. 

266 


MEASUREMENT      OF      GAS      AND      AIR 

In  case  the  differential  and  static  pressures  vary  over  wide 
ranges,  this  method  is  not  satisfactory  due  to  the  fact  that 
the  results  will  be  considerably  higher  than  the  true  result. 
For  very  wide  variations  the  charts  should  be  averaged  for 
fifteen  minute  periods  and  extensions  for  the  fifteen  minute 
periods  should  be  made  to  obtain  accurate  results. 

Quite  frequently  a  planimeter  and  reference  chart  is  used 
to  obtain  the  average  differential  reading  and  average  static 
reading.  The  results  obtained  by  this  method  are  as  ac- 
curate as  those  obtained  by  averaging  the  differential  and 
static  pressure  records  for  the  day  and  then  obtaining  the 
average  extension,  which  extension  is  multiplied  by  the 
number  of  hours  for  which  the  average  was  obtained.  This 
method  eliminates  the  necessity  of  recording  the  differential 
and  static  pressures  on  the  chart  and  greatly  simplifies  the 
work.  It  should  only  be  used  when  the  static  pressures  or 
differential  pressures  do  not  vary  over  wide  limits,  as  the 
results  in  such  cases  will  be  greater  than  the  true  result. 

If,  for  any  reason,  the  meter  is  out  of  service  for  a  period 
during  which  the  gas  has  been  flowing,  the  average  reading 
for  the  period  prior  to  shut  down  and  ^iter  shut  down  should 
be  used  for  the  period  of  the  shut  down. 

ORIFICE  METER  CALCULATOR 

As  has  been  previously  explained,  the  best  method  of 
reading  and  calculating  the  charts  for  the  determination 
of  flow,  is  to  obtain  the  pressure  extension  for  each  period 
and  add  these  pressure  extensions  together  and  multiply  by 
the  coefficient.  It  has  also  been  explained  that  the  method 
of  averaging  the  differential  pressure  for  the  day,  the  static 
pressure  for  the  day,  and  using  these  averages  for  the  cal- 
culation of  the  flow,  will  often  produce  a  considerable  error 
if  the  static  or  differential  pressures  vary  over  a  wide  range 
during  the  day.  The  use  of  the  planimeter  or  averaging 
instrument  is  also  open  to  the  same  objection  and  does  not 

267 


MEASUREMENT      OF      GAS      AND       AIR 


Co  ft. 

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MEASUREMENT      OF      GAS      AND      AIR 

in  any  way  increase  the  accuracy  but  will  produce  about  the 
same  accuracy.  To  simplify  all  work  and  obtain  an  instan- 
taneous value  of  the  flow  for  each  hour,  or  smaller  period  if 
desired,  a  calculator  has  been  placed  on  the  market. 

By  using  this  instrument  the  operator  can  place  the  chart 
in  proper  position  on  the  instrument  and  determine  the 
flow  for  any  hour  during  the  day  without  any  calculations 
whatever.  That  is: — the  instrument  adds  14.4  to  the  static 
reading  and  multiplies  the  square  root  of  this  value  by  the 
square  root  of  the  differential  by  the  coefficient  of  the  disc 
at  one  setting  giving  the  hourly  flow. 

The  operation  of  the  instrument  is  as  follows:  The 
chart  is  placed  on  the  instrument,  the  sliding  scale  is  moved 
so  that  the  value  of  the  coefficient  is  opposite  the  indicating 
mark  on  the  lever,  and  without  any  further  alteration  for 
each  chart  the  lever  is  moved  until  the  hair  line  on  the 
transparent  indicator  is  over  the  average  differential  reading. 
The  operator  then  reads  the  hourly  flow  opposite  the  static 
pressure  on  the  scale.  This  hourly  flow  is  registered  on  an 
adding  machine.  The  chart  is  moved  one  hour  ahead,  lever 
moved  so  that  the  indicator  is  over  the  differential  reading  for 
the  following  hour,  he  looks  opposite  the  static  pressure  for 
that  hour  on  the  scale  and  obtains  the  reading  which  is 
placed  on  the  adding  machine.  For  the  third  hour,  the 
lever  is  moved  until  the  indicator  is  over  the  differential 
reading  for  the  third  hour  and  opposite  the  static  pressure, 
he  obtains  the  reading  on  the  diagram  and  adds  this  value 
on  the  adding  machine,  etc.  At  the  end  of  the  24  hour 
period  the  total  result  is  added  and  the  volume  per  day  is 
read  from  the  adding  machine.  This  eliminates  any  ex- 
tended calculations,  eliminates  the  necessity  of  the  operator 
reading  the  differential  pressure  and  carrying  these  readings 
in  his  mind  and  obtaining  the  extension  from  an  extension 
book.  In  fact  all  laborious  work  involved  in  calculating 
orifice  meter  charts  is  eliminated. 


MEASUREMENT      OF      GAS      AND      AIR 


LOCATION— Lyons  No.  6. 

Meter  No.  241  Orifice  No.  Ml 790 T  Month— March, 

Internal  Diameter  of  Pipe  4-026"  Diameter  Orifice  2" 

Pressures  at  2J/2  and  8  Diameter  Connections. 
Atmospheric  Pressure  144.  Temperature  60  deg.  fahr. 

Pressure  Base  10  oz.          Coefficient,  1261.3         Specific  Gravity  . 
Remarks — Gas  Tested  3-10- '21.  Specific  Gravity,  0.68 

1261.3  x  .9393=1184.7  Revised  Coefficient  used  after  10th. 


Date 

Pressure 
Extension 

Coeffi- 
cient 

Quantity                     Remarks 

1 

774.97 

1261.3 

£77^70. 

2 

752.31 

" 

948889. 

3 

736.94 

" 

929502. 

4 

715.23 

1  * 

902120. 

5 

692.14 

" 

872996. 

6 

676.33 

" 

853055. 

7 

672.86 

" 

848678. 

8 

663.54 

'  ' 

836923. 

9 

654-92 

" 

826051. 

10 

643.41 

" 

811533.   | 

11 

632.16 

1184.7 

748920. 

12 

681.02 

" 

806804.   ' 

13 

762.45 

" 

903274- 

14 

808.97 

" 

958387. 

15 

16 

17 

18 

i 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

Fig.  114 

270 

PART    FIVE 

MEASUREMENT     OF    STEAM 


An  orifice  meter  will  measure  the  flow  of  any  gas,  vapor 
or  liquid  of  fairly  uniform  gravity  at  high  pressure  or  under 
a  vacuum.  It  is  especially  adaptable  for  the  measurement 
of  steam  as  the  properties  peculiar  to  steam  simplify  all 
calculations  to  a  minimum.  Being  a  weight  measuring 
instrument  as  well  as  a  volume  instrument,  as  will  be  shown 
later,  it  becomes  the  nearest  approach  to  a  perfect  flowing 
fluid  weighing  machine  and  steam  power  recording  instru- 
ment. It  automatically  weighs  the  moisture  in  unsaturated 
steam  and  even  though  the  amount  of  moisture  or  superheat 
in  the  steam  is  unknown,  the  power  as  determined  is  approxi- 
mately correct  for  the  reason  that  the  correcting  factors  are 
very  small  for  relatively  large  amounts  of  moisture  and  super- 
heat. 

The  great  advantage  in  using  the  type  of  meter  which  is 
used  for  measuring  gas  is  that  the  operator  obtains  a  defi- 
nite continuous  record  of  the  pressure  in  the  line  as  well  as 
the  flow.  Flow  meters  do  not  give  a  pressure  record  on  the 
same  chart,  this  information  must  be  obtained  from  an  in- 
dependent pressure  gauge. 

Furthermore,  it  is  the  consensus  of  opinion  of  engineers 
that  the  orifice  will  give  more  consistent  results  than  can  be 
obtained  by  the  pitot  tube  or  a  modification,  and  the  flow 
nozzle.  The  ease  of  installation  of  the  plain  orifice,  as 
compared  with  the  nozzle,  has  made  a  distinct  appeal  to 
the  steam  engineer. 

271 


MEASUREMENT      OF      STEAM 

For  a  description  of  the  orifice  meter  the  reader  is  referred 
to  Part  3.  This  Part  precedes  the  following  details  which 
apply  to  steam. 

The  Differential  Gauge  records  on  a  chart  the  differential 
pressure  between  the  pressure  connections,  and  the  static 
pressure  at  one  of  the  connections.  These  factors  with  the 
area  of  the  orifice  enable  us  to  determine  the  flow  from  the 
formula : 

W  =  C  VT7 

Where  W^  =  the  quantity  of  steam  passing  the  orifice.  The 
result  can  be  expressed  in  "pounds"  or 
"pounds  from  and  at  212  deg.  fahr." 

C  =  the  Hourly  Orifice  Coefficient  for  steam.  The 
value  of  this  term  remains  the  same  for  each 
installation  and  basis  of  measurement. 

h  =  the  differential  pressure  existing  between  the  two 
pressure  connections  expressed  in  inches  of 
water  head,  this  value  being  recorded  graph- 
ically on  the  chart  of  the  recording  differen- 
tial gauge. 

P  =  the  static  pressure  expressed  in  absolute  units, 
being  equal  to  the  gauge  pressure  (which  is 
recorded  on  the  chart)  plus  the  atmospheric 
pressure.  The  value  of  the  gauge  pressure  is 
also  recorded  on  the  chart. 

The  value  of  the  Hourly  Orifice  Coefficient  C  in  the 
above  formula  is  found  on  Pages  282  and  287,  computed  for 
various  diameters  of  orifice  and  diameters  of  pipe,  these  values 
having  been  determined  by  exhaustive  experimental  and 
practical  tests  in  comparison  with  actual  displacement.  The 
extensions  of  the  values  of  V  hP  have  been  compiled  and 
are  given  in  the  book  entitled  "Pressure  Extensions"  pub- 
lished by  this  Company. 

272 


MEASUREMENT      OF      STEAM 

Example — One  hour  reading  (weight  desired) : 

Average  differential  reading  h  =  25  inches. 

Diam.  of  Pipe  =  4  inches.     Diam.  of  Orifice  =  2  inches. 

Average  Gauge  Pressure  p  =  9Q  pounds. 

Hourly  Orifice  Coefficient  C  =  48. 19  for  2  inch  orifice  in  a 
4  inch  line,  (Page  282). 


Weight  per  hour,  W  =  48.19  V 25 X  (90 +14. 4) 

Orifice         Pressure 

=  48.19X51.088  =  2462  pounds. 

Coefficient.   Extension. 

If  the  heat  content  or  power  is  desired  (using  the  same 
data  with  feed  water  temperature  at  62  deg.  fahr.)  the 
Hourly  Orifice  Coefficient  C  is  57.55  for  a  2  inch  orifice  in  a 
4  inch  line,  (Table  55,  Page  287). 

Orifice  Pressure 


W  =  57.55  V  25  X  (90  +14.4)  =57.55  X  51.088 

Coefficient.     Extension. 

or  the  power  passing  through  the  orifice  =  2940  "pounds 
from  and  at  212  deg.  fahr."  per  hour. 

Therefore,  the  Power  flowing  in  the  line  is  equal  to  the 
Coefficient  of  the  Disc  multiplied  by  the  Pressure  Extension. 

The  relation  between  the  differential  pressure  and  the 
velocity  of  the  fluid  through  the  orifice  is  expressed  by  the 
formula  : 

v=c 


v 


Where    V  =  velocity  of  flowing  fluid  in  feet  per  second. 

g  =  acceleration  due  to  gravity  in  feet  per  sec.,  per 

sec.  =  32.  16. 
H  =  differential  expressed  in  feet  head  of  flowing  fluid. 


The  well  known  formula  V  =  V  2  gH  expresses  the  theo- 
retical flow  eliminating  friction  and  other  influences.  When 
applied  to  actual  conditions  a  multiplier  is  used  to  take 
care  of  the  influences  due  to  contraction  of  jet,  friction, 

273 


MEASUREMENT      OF      STEAM 

etc.  This  factor  Cv  is  commonly  known  as  the  "coefficient 
of  velocity."  This  formula  may  be  applied  directly  for 
measurement  as  in  the  following  example. 

Atmospheric  Pressure  14.7.  Line  Pressure,  100  Ib.  Gauge. 
Diameter  of  Orifice,  3  inches.  Diameter  of  Pipe,  6.065 
inches.  Differential,  2  inches  of  Mercury.  Pressure  Con- 
nections, 2  J/2  and  8  diameters  from  the  orifice,  no  moisture 
in  the  steam. 

O   QQ 

Ratio  of  diam.  of  orifice  to  diam.  of  pipe  =  — =  .495 

6.065 

Cv  for  .495  ratio  =734. 

For  the  measurement  of  steam,  the  gauge  connections 
to  the  gauge  are  filled  with  water  as  in  measuring  liquids  and 
consequently  each  inch  of  mercury  differential  is  offset  by 
an  inch  of  water  so  that  2  inches  of  mercury  pressure  as  in- 
dicated is  equal  to  (2X12.6  =  25.2)  25.2  inches  of  water 
differential. 

As  one  cubic  foot  of  steam  at  100  Ib.  gauge  pressure 

62  35 

weighs  0.257  Ib.  per  cu.  ft.  one  foot  head  of  water  equals  — - — 

0.257 

or  243  feet  head  of  steam  and  one  inch  of  water  equals  20.25 
feet  of  steam  head  at  an  absolute  pressure  of  14.7  Ib.  per 
square  inch. 

Therefore,  #  =  20.25X25.2  or  510  feet  head  of  steam. 


Therefore,    V  =  CV  V  2g#  =  .734  V2X32.16X510=  132.9 
ft.  per  second. 

Area  of  the  orifice  =  .0491  sq.  ft.      Page  75. 

Quantity  =  areaXvelocity  =  .049lXl32.9  =  6.53  cu.  ft.  per 
second. 

Weight  =  volume  in  cubic  feetX  weight  per  cubic  foot  = 
6.53X0.257  =  1.68  Ib.  per  second  =  6050  Ib.  per  hour. 

274 


MEASUREMENT      OF      STEAM 


In  the  formula  V  =  CV^2  gH  the  differential  head  is  ex- 
pressed in  feet  head  of  flowing  fluid.  As  it  is  not  practical 
to  register  this  value  directly,  the  differential  is  recorded 
on  the  chart  in  inches  of  water  pressure.  If  steam  is 
flowing  in  a  line  under  a  pressure  of  100  pounds  gauge,  the 
weight  of  a  cubic  foot  of  steam  is  0.257  Ib.  and  as  water 
weighs  62.35  Ib.  per  cubic  foot  or  243  times  as  much,  one 
foot  of  water  pressure  is  equivalent  to  243  feet  head  of  steam 
at  100  Ib.  pressure;  one  inch  of  water  pressure  is  equal  to 
one-twelfth  of  243  feet  or  20.25  feet  of  steam  head  and  20 
inches  of  water  head  would  equal  20  times  20.25  feet  or  405 
feet  head  of  steam  at  100  pounds  gauge.  This  relation  may 
be  expressed  by  the  following  formula: 


12  w 

Where   H  =  differential  in  feet  head  of  flowing  steam. 

ww  =  weight  of  water  in  pounds  per  cubic  foot  =  62.35. 

h  =  differential  in  inches  of  water  pressure. 

12  =  number  of  inches  in  a  foot. 

w  =  weight  of  flowing  steam  in  pounds  per  cu.  ft. 
The  above  example  can  be  written  thus  : 

„     62.35X20 

H  =  -      —    =405  feet  steam  head. 
12X0.257 


Substituting  the  value  of  H  in  the  formula  V  =  CV^ 
We  obtain  7=  Cv 


wh_         (2X32.16X62.35  h 
-C'\-      —^r- 


or  7=18.2810, 

"  w 


This  expreSvSion  forcibly  illustrates  the  fact  that  the  ve- 
locity depends  upon  the  weight  per  cubic  foot  of  the  fluid. 
As  the  weight  per  cubic  foot  increases,  the  velocity  decreases 
when  the  differential  pressure  is  a  constant. 

275 


MEASUREMENT      OF      STEAM 

Or  using  a  plain  illustration  with  the  same  force  applied, 
a  ball  containing  a  cubic  foot  of  lead  will  move  with  less 
speed  or  velocity  than  a  ball  containing  the  same  quantity 
of  wood. 

The  weight  of  steam  passing  the  orifice  per  hour  is  equal 
to  the  area  of  the  orifice  in  square  feet  multiplied  by  the 
velocity  in  feet  per  hour  multiplied  by  the  weight  per  cubic 
foot.  This  fact  may  be  expressed  by  the  following  formula  : 

0.7854  d2         QQV 
144 


Wi  =  19.635 

Where  Wi  =  actual  weight  of  steam  passing  the  orifice  in 
pounds  per  hour. 

0.7854  f 

—  =  area  of  orifice  in  square  feet. 
144 

d  =  diameter  of  orifice  in  inches. 
144  =  number  of  square  inches  in  a  square  foot. 
3600  =  seconds  in  one  hour. 

V  =  velocity  of  fluid  through  orifice  in  feet  per  sec. 

Substituting  the   value  of   V  where  7=18.281    C,  J— 
in  the  expression,  W^  =  19.635  d2XVXw 


Wi  =  19.635  (FX  18.281  C,  \—Xw 

"  w 

JFi  =  358.95  C,d2  VAw 

This  expression  is  true  for  any  gas,  vapor  or  liquid. 

When  measuring  steam  with  an  Orifice  Meter  the  con- 
necting lines  and  the  gauge  itself  would  be  partially  filled 
with  condensed  water,  which  would  create  an  erroneous 
differential  reading  if  the  head  of  water  acting  on  the  two 

276 


MEASUREMENT      OF      STEAM 


Table  52-PROPERTIES  OF  SATURATED  STEAM 


Temp. 
Deg.Fahr. 

Heat  of 
the  Liquid 

Latent 
Heat 

Total 
Heat 

Weight  of  1 
Cubic 
Foot,  Lb. 

Volume  of 
1  U>.( 
Cubic  Feet 

Vacuum 

T_        TV/T^*- 

t 

h 

L 

H 

5 

Q 

An.   Jvier. 
25 

133.2 

101.1 

1017.0 

1118.1 

.00689 

145.2 

20 

161.2 

129.0 

1001.0 

1130.0 

.0133 

75.2 

15 

178.9 

146.8 

990.4 

1137.2 

.0195 

51.1 

10 

192.2 

160.1 

982.6 

1142.7 

.0255 

39.7 

5 

202.9 

170.9 

975.9 

1146.8 

.0314 

31.8 

GaugePres. 

0 

212.0 

180.0 

970.4 

1150.4 

.0373 

26.8 

5 

227.2 

195.3 

960.6 

1155.9 

.0491 

20.38 

10 

239.4 

207.7 

952.5 

1160.2 

.0607 

16.40 

15 

249.8 

218.2 

954.5 

1163.7 

.0721 

13.87 

20 

258.8 

227.4 

939.2 

1166.6 

.0834 

11.99 

25 

266.8 

235.6 

933.6 

1169.2 

.0946 

10.57 

30 

274  .  1 

243.1 

928.5 

1171.6 

.1058 

9.47 

35 

280.6 

249.7 

923.8 

1173.5 

.1168 

8.56 

40 

286.7 

256.0 

919.3 

1175.3 

.1278 

7.82 

45 

292.4 

261.8 

915.2 

1177.0 

.1387 

7.20 

50 

297.7 

267.2 

911.2 

1178.4 

.1497 

6.68 

55 

302.6 

272.3 

907.4 

1179.7 

.1605 

6.23 

60 

307.3 

277.1 

903.9 

1181.0 

.1714 

5.83 

65 

311.8 

281.7 

900.5 

1182.2 

.1823 

5.49 

70 

316.0 

286.0 

897.3 

1183.3 

.1930 

5.18 

75 

320.1 

290.3 

894.1 

1184.4 

.2041 

4.91 

80 

323.9 

294.3 

891.1 

1185.4 

.2145 

4.66 

85 

327.6 

298.1 

888.2 

1186.3 

.2252 

4.44 

90 

331.2 

301.8 

885.4 

1187.2 

.2358 

4.24 

95 

334.6 

305.3 

882.6 

1187.9 

.2465 

4.05 

100 

337.9 

308.8 

880.0 

1188.8 

.2570 

3.89 

105 

341.1 

312.1 

877.4 

1189.5 

.2677 

3.735 

110 

344.2 

315.3 

874.9 

1190.2 

.2785 

3.592 

115 

347.2 

318.4 

872.5 

1190.9 

.2890 

3.460 

120 

350.1 

321.5 

870.1 

1191.6 

.2996 

3.338 

125 

352.9 

324.4 

867.8 

1192.2 

.3101 

3.226 

130 

355.6 

327.2 

865.6 

1192.8 

.3207 

3.118 

135 

358.3 

330.0 

863.4 

1193.4 

.3314 

3.018 

140 

360.8 

332.7 

861.2 

1193.9 

.3419     ' 

2.925 

145 

363.4 

335.4 

859.0 

1194.4 

.3523 

2.839 

150 

365.9 

338.0 

857.0 

1195.0 

.3627 

2.758 

155 

368.4 

340.6 

854.8 

1195.4 

.3732 

2.680 

160 

370.7 

343.1 

852.8 

1195.9 

.3837 

2.606 

165 

373.0 

345.5 

850.9 

1196.4 

.  3942 

2.537 

170 

375.3 

347.9 

848.9 

1196.8 

.4046 

2.472 

175 

377.5 

350.3 

847.0 

1197.3 

.4151 

2.410 

180 

379.7 

352.5 

845.1 

1197.7 

.4256 

2.350 

185 

381.8 

354.8 

843.3 

1198.1 

.4364 

2.294 

190 

383.9 

357  .  0 

841.5 

1198.5 

.4464 

2.240 

195 

385.9 

359.1 

839.7 

1198.8 

.4564 

2.190 

200 

387.9 

361.3 

838.0 

1199.3 

.4670 

2.141 

210 

391.8 

365.4 

834  .  5 

1199.9 

.488 

2.049 

220 

395.5 

369.3 

831.2 

1200.5 

.508 

1.966 

230 

399.2 

373.2 

828.0 

1201.2 

.529 

1.889 

240 

402.6 

376.9 

824.8 

1201.7 

.550 

1.818 

250 

406.1 

380.6 

821.7 

1202  .  3 

.570 

1.752 

277 


MEASUREMENT      OF      STEAM 


portions  of  the  gauge  were  not  equal.  To  make  the  heads 
equal,  a  reservoir  R  made  of  a  12  inch  length  of  3  inch  pipe 
and  two  caps,  is  installed  on  each  gauge  line.  These  reser- 
voirs are  placed  horizontal  on  the  same  level,  above  the  gauge 
and  connections,  tapped  in  the  center  of  one  of  the  caps  for 
connections  to  the  main  and  in  the  bottom  for  connections 
in  the  gauge.  When  the  steam  enters  the  connections, 
reservoirs,  and  gauge,  it  will  condense  as  these  are  not  insu- 
lated or  jacketed,  and  in  a  short  time  the  water  will  fill  both 
portions  of  the  gauge,  connections  between  the  gauge  and 


115— SKETCH    OF    ORIFICE    METER    INSTALLATION 
MEASURING  STEAM  IN  A  VERTICAL  LINE 


FOR 


the  reservoirs,  and  the  lower  portion  of  the  reservoirs,  any 
excess  condensate  returning  to  the  main  through  connec- 
tions A  C  and  B  D.  These  connections  always  slope  toward 
the  main  to  avoid  trapping  any  water.  Therefore,  since  the 
inlets  to  the  reservoir  which  become  the  outlets  for  excess 
condensation  are  on  the  same  level,  the  water  pressures  on 
each  portion  of  the  gauge  are  equal  and  balance  one  another 
for  all  differentials.  When  the  differential  h  increases  the 
water  level  at  A  is  lowered  and  at  B  is  raised,  causing  a  por- 
tion to  flow  through  the  connection  B  D  into  the  main.  In 

278 


MEASUREMENT      OF      STEAM 

the  meantime  additional  condensation  is  filling  the  reservoir  A 
to  the  outlet  level.  This  change  of  levels  in  the  reservoir, 
for  the  short  period  of  time  it  does  exist,  is  immaterial  for 
the  reason  that  a  volume  of  water  equivalent  to  }^  inch  in 
depth  of  the  reservoir  is  sufficient  to  fill  the  space  vacated  by 
the  mercury  throughout  the  total  range  of  the  gauge. 

Due  to  the  fact  that  the  recording  gauges  are  filled  with 
water  each  inch  of  mercury  differential  is  partially  counter- 
balanced by  an  inch  of  water  and  therefore  each  inch  of 
mercury  differential  is  equivalent  to  only  12.6  inches  of 


•Direction  off/ow 


Fig.    116— SKETCH    OF    ORIFICE    METER    INSTALLATION    FOR 
MEASURING  STEAM  IN  A  HORIZONTAL  LINE 


water  differential  instead  of  13.6  inches  which  would  be  the 
case  if  the  water  did  not  fill  the  connections.  Therefore 

1  O  £5 

a  correcting  factor  — —  must  be  introduced  and  the  differen- 
13.6 

tial  h  be  multiplied  by  this  factor,  for  the  reason  that  the 
gauges  are  constructed  to  indicate  13.6  inches  of  water  pres- 
sure differential  for  each  inch  of  mercury  differential. 

279 


MEASUREMENT      OF      STEAM 


280 


MEASUREMENT      OF      STEAM 


281 


MEASUREMENT      OF      STEAM 


Table  53— HOURLY  ORIFICE  COEFFICIENTS 
FOR  STEAM 

Pressures  taken  2^  diameters  upstream  and  8  diameters  downstream. 
Values  of  C  in  Wi=  C  VhP  where  Wi=actual  weight  of  saturated  steam  pass- 
ing orifice  in  pounds  per  hour. 

Size  of  meter  is  diameter  of  pipe  line  in  which  orifice  is  placed. 
See  Table  54  for  correcting  factors. 


Diameter 
of 


Diameter  of  Pipe  Line 


Orifice 
Inches 

4" 

6" 

8" 

10" 

M 

5/e 

2.515 
3  950 

2.500 

2.492 

2.490 

% 

V* 

5.725 
7  857 

5.654 

5.631 

5.617 

V/8 

IX 
i*A 

VA 
i«l 

10.36 
13.26 
16.58 
20.33 
24.58 
29.40 

10.13 
15~99 
23*32 

10.06 
15.80 
'22.'9l' 

10.02 
15~72 

'22^72' 

1% 

iii 

34.90 

41  14 

32.20 

31.44 

31.08 

2 

21A 

48.19 
56  23 

42.74 

41.43 

40.84 

fyi 

2*/8 

2y2 

2% 
2% 

2Ve 

65.36 
76.15 
87.76 
101.5 
117.3 
135  2 

55.27 
69^99 

'87^52' 

53.04 
66~24 
81.25 

52.05 
64^71' 
'78^95 

3 

3M 

155.8 

108.1 
132.7 

98.28 
117.5 

94.79 
112.1 

BH 

162  1 

139  5 

131.8 

3/i 

197  0 

164.3 

153.3 

4 

4M 
4^ 
4^ 
5 
514 

238.8 
288.6 
347.9 

192.4 
224.7 
260.9 
303.1 
350.2 
405  4 

177.0 
203.1 
232.1 
264.0 
299.3 
338.7 

51A 

468.4 

381.6 

&A 

539.3 

430.2 

6 

6M 

620.8 

483.4 
542.8 

Q1A 

609.2 

6% 

683.1 

7 

765.7 

7M 

856.9 

7^ 

957.3 

282 


MEASUREMENT      OF      STEAM 


Table  54 

MULTIPLIERS  FOR  VARIOUS  GAUGE  PRESSURES, 
MOISTURE,  AND  SUPERHEAT 


Used  with  Table  53. 


Percent- 

Static  Pressure  Pounds  Gauge 

Moisture 

25 

50 

100 

150 

200 

250 

30 

1.232 

1.214 

1.195 

1.184 

1.177 

1.173 

25 

1.191 

1.173 

1.155 

1.145 

1.138 

1.134 

20 

1.153 

1.135 

1.117 

1.107 

1.100 

1.097 

15 

1.119 

1.102 

1.085 

1.075 

1.069 

1.064 

10 

1.087 

1.071 

1.054 

1.045 

1.038 

1.034 

5 

1.058 

1.042 

1.026 

1.017 

1.011 

1.007 

3 

1.046 

1.031 

1.015 

1.006 

1.000 

.997 

2 

1.041 

1.026 

1.010 

1.001 

.995 

.992 

1 

1.036 

1.021 

1.005 

.996 

.990 

.987 

0 

1.031 

1.016 

1.000 

.991 

.985 

.981 

Super- 

heat 

deg.  fahr. 

20 

1.016 

1.001 

.985 

.976 

.970 

.967 

50 

.992 

.978 

.961 

.952 

.945 

.940 

100 

.950 

.945 

.929 

.919 

.911 

.904 

150 

.930 

.915 

.899 

.889 

.882 

.877 

200 

.902 

.890 

.874 

.863 

.855 

.846 

250 

.878 

.866 

.850 

.839 

.832 

.826 

300 

.855 

.843 

.829 

.819 

.811 

.805 

400 

.818 

.806 

.792 

.781 

.773 

.768 

500 

.781 

.770 

.760 

.750 

.743 

.737 

The  weight  of  steam  per  cubic  foot  varies  approximately 
with  the  absolute  pressure. 

w  =  .  002241  P 
Where  w  =  weight  of  steam  in  pounds  per  cubic  foot. 

P  =  the  static  pressure  of  steam  expressed  in  abso- 
lute units  being  equal  to  the  gauge  pressure  plus 
the  atmospheric  pressure. 


MEASUREMENT      OF      STEAM 


Substituting  these  factors  in  T^i  =  358.95  Cvd  V  h  w 


nr      u*  -    w/      OKQOK   ^^2      12.6  AX. 002241  P 
We  obtain  T7 1  =  358. 95  Cvd\\- 

*  13.6 

or  JFi  =  16.36  C^2  VTP  =  C  VTP 

Where  TFi  is  equal  to  the  actual  weight  of  dry  steam  pass- 
ing the  orifice  in  pounds  per  hour. 

The  Hourly  Orifice  Coefficient,  C  in  Table  53,  is  equal  to 
16.36  Cvd2. 

The  multipliers  for  revision  of  the  Coefficients  are  de- 
termined by  substituting  the  weight  of  the  unsaturated  or 
superheated  steam  in  pounds  per  cubic  foot  (Page  277,)  for 
w  in  the  formula.  These  multipliers  may  be  applied  either 
to  the  coefficient  or  the  calculated  result. 

The  main  purpose  in  measuring  steam  is  to  determine 
the  amount  of  heat  or  power  furnished  by  the  boiler  and 
supplied  to  the  heat  or  power  consuming  units.  The 
amount  of  steam  power  produced  and  consumed  is  ex- 
pressed in  "pounds  from  and  at  212  deg.  fahr."  This  term 
is  a  steam  engineer's  unit  of  measurement  just  as  one  of  the 
units  for  the  measurement  of  gas  is  a  "cubic  foot  at  60  deg. 
fahr.  at  4  ounces  pressure."  The  expression  "pound  from  and 
at  212  deg.  fahr."  is  a  unit  of  heat  measurement  being  equal  to 
970.4  B.  t.  u.,  the  number  of  heat  units  required  to  convert 
one  pound  of  water  "from"  212  deg.  fahr.  into  dry  steam 
"at"  that  temperature.  A  boiler  horse  power  is  equivalent 
to  34 y%  "pounds  of  steam  from  and  at  212  deg.  fahr."  The 
number  of  "pounds  from  and  at  212  deg.  fahr."  may  be 
either  greater  or  less  than  the  actual  weight.  For  example, 
it  takes  11587  B.  t.  u.  to  convert  10  Ib.  of  water  from  62  deg. 
fahr.  into  dry  steam  at  100  Ib.  gauge  pressure  and  therefore 
the  heat  supplied  to  or  the  power  content  of  the  10  Ib.  of 
steam  is  equal  to  11587  B.  t.  u.  divided  by  970.4  B.  t.  u.  or 
11.94  "pounds  from  and  at  212  deg.  fahr."  If  the  tempera- 

284 


MEASUREMENT      OF      STEAM 

ture  of  the  water  were  72  deg.  fahr.  or  10  degrees  higher 
than  the  previous  instance,  the  heat  absorbed  would  be 
11487  B.  t.  u.  or  equal  to  11.83  "pounds  from  and  at  212  deg. 
fahr.,"  about  1  per  cent  less.  Although  the  actual  weight 
is  not  changed  the  heat  absorbed  does  change.  The  heat 
content  of  1  Ib.  of  steam  at  100  Ib.  gauge  pressure  above 
water  at  a  temperature  of  62  deg.  fahr.  is  1158.7  B.  t.  u. 
and  at  250  Ib.  pressure  is  1172.2  B.  t.  u.  above  same  temp- 
erature base.  In  other  words,  the  unit  "pounds  from  and 
at  212  deg.  fahr."  is  the  steam  engineer's  "yard  stick."  The 
power  passing  through  the  line  could  be  expressed  in  B.  t.  u. 
just  as  well  as  in  "pounds  from  and  at  212  deg.  fahr,"  except 
that  the  B.  t.  u.  unit  is  so  small.  Furthermore,  this  expres- 
sion has  become  firmly  established  in  the  steam  engineers' 
vocabulary  by  universal  usage. 

Just  as  in  measuring  gas  or  any  fluid,  whose  volume  per 
pound  is  affected  by  pressure  and  temperature,  bases  are 
established,  so  in  measuring  steam  a  temperature  base  is 
established  from  which  all  calculations  are  made.  In  gas 
measurement  an  average  temperature  of  60  deg.  fahr.  and  an 
atmospheric  pressure  14.4  Ib.  per  sq.  in.  are  used  as  bases.  In 
calculating  the  value  of  the  Hourly  Orifice  Coefficients  for  the 
measurement  of  the  flow  of  steam  (Page  287)  we  have  used  62 
deg.  fahr.  (a  low  feed  water  temperature)  as  a  temperature 
base  above  which  the  heat  content  is  expressed. 

The  heat  content  of  steam  for  various  pressures  may  be 
found  in  the  Table  of  Properties  of  Steam,  Page  277.  The 
total  heat  content  of  steam  for  various  pressures  in  this 
table  is  expressed  above  a  temperature  base  of  32  deg.  fahr. 
and  to  change  to  a  base  of  62  deg.  fahr.  30.1  B.  t.  u.  should 
be  subtracted.  The  total  heat  content  of  steam  at  100  Ib. 
gauge  pressure  is  1188.8  minus  30.1  or  1158.7  B.  t.  u.  above 
a  temperature  base  of  62  deg.  fahr. 

To  express  the  weight  on  the  basis  of  heat  units  or  W 
weight  per  hour  in  "pounds  from  and  at  212  deg.  fahr," 

285 


MEASUREMENT      OF      STEAM 

we  assume  an  average  heat  content  of  saturated  steam  per 
pound  for  all  pressures  as  1158.7  B.  t.  u.  above  a  temper- 
ature base  of  62  deg.  fahr.  This  is  an  approximation  but  the 
net  effect  of  using  this  value  nearly  cancels  the  error  in- 
volved in  assuming  the  value  of  w  as  equal  to  .002241  P  for 
all  pressures. 

B.  t.  u.  per  pound  "from  and  at  212  deg.  fahr. "  =  970. 4. 

Then  one  pound  of  steam  =  — '—^—  =  1.194  "pounds  from 

970.4 

and  at  212  deg.  fahr." 
Or  JF  =  1.194  multiplied  by  the  actual  weight. 

Where   W  =  quantity  of  steam  passing  the  orifice  per  hour 
in  "pounds  from  and  at  212  deg.  fahr." 

W  =  1. 194  X  16.36  Cv<f^lhJ 
W  =  19.53  CjF^JTP 

in  which  formula  19.53  Cvd2  is  equal  to  the  value  of  C,  the 
coefficient  published  in  the  Table  of  Hourly  Orifice  Co- 
efficients for  Steam  on  Page  287.  In  this  Table  a  separate 
value  is  given  for  each  diameter  of  orifice  and  each  size  of  line, 
the  value  of  C  varying  as  the  square  of  the  diameter  of 
orifice  and  directly  with  the  value  of  Cv,  Cv  being  dependent 
upon  the  ratio  of  the  size  of  the  orifice  to  the  size  of  the  pipe. 
Its  value  has  been  determined  experimentally  for  all  ratios. 
In  case  the  steam  contains  moisture  its  weight  per  cubic 
foot  increases  but  this  increase  is  more  than  offset  by  the 
decrease  in  the  number  of  heat  units  contained  in  a  pound 
and  therefore  the  multiplier  is  less  than  1  instead  of  greater, 
in  expressing  the  power  in  "pounds  from  and  at  212  deg. 
fahr."  In  the  case  of  superheat  the  weight  per  cubic  foot 
decreases  more  rapidly  than  the  heat  content  per  pound 
increases  making  the  correcting  factor  less  than  unity 
instead  of  greater. 


MEASUREMENT      OF      STEAM 


Table  55— HOURLY  ORIFICE  COEFFICIENTS 
FOR  STEAM 

Pressures  taken  2^  diameters  upstream  and  8  diameters  downstream. 
Values  of  C  in  W  =  C  VhP  where  W  expresses  quantity  passing  through  orifice 

in  "pounds  of  steam  from  and  at  212  deg.  fahr." 
Size  of  Meter  is  diameter  of  pipe  line  in  which  orifice  is  placed. 
Heat  content  calculated  above  62  deg.  fahr. 


Diameter 
of 


Diameter  of  Pipe  Line 


Orifice 
Inches 

4" 

6" 

8" 

10" 

K 

5% 

3.003 
4  716 

2.985 

2.976 

2.973 

ZA 
V* 

6.836 
9.382 

6.751 

6.723 

6.706 

I 
11A 

12.37 
15.83     . 

12.10 

12.01 

11.97 

M 

l*A 

19.79 
24.28 

19.10 

18.87 

18.77 

m 

15A 

29.35 
35.10 

27.84 

27.36 

27.13 

1% 

\TA 

41.67 
49.12 

38.44 

37.54 

37.12 

2 
2U 

57.55 
67.14 

51.04 

49.47 

48.76 

2H 

IV* 

78.04 
90  93 

66.00 

63.33 

62.15 

2^ 
2% 

104.8 
121.2 

83.57 

79.10 

77.27 

2M 

2% 

140.1 
161.5 

104.5 

97.01 

94.27 

3 

3^ 
3^ 

? 

186.1 

129.1 
158.4 
193.5 
235.2 

285.1 

117.3 
140.3 
166.6 
196.1 

229.8 

113.2 
133.9 
157.4 
183.1 
211.3 

4M 

344.6 

268.3 

242.5 

4U 

415.4 

311.6 

277.1 

43x; 

361  9 

315  2 

5 

418  2 

357  4 

514 

484  1 

404  4 

5^ 
53/^ 

559.2 
643  9 

455.6 
513  6 

6 

741  3 

577  2 

61^ 

648  1 

§V> 

727  4 

&A 

815  6 

7 

914  3 

7V* 

1023 

iy2 

1143. 

287 


MEASUREMENT      OF      STEAM 


Table    56— MULTIPLIERS    FOR    GAUGE    PRESSURE, 

MOISTURE,  SUPERHEAT  AND    FEED  WATER 

TEMPERATURE 

To  be  used  in  connection  with  Table  55. 


Gauge 
Pressure 
Pounds 

Percentage 

of 

Moisture 

Saturated 
Steam 

Superheat  deg. 

fahr. 

20 

15 

10 

5 

50 

100      200 

300 

500 

25 

50 

100 

150 

250 


Feed  Water  Temperature  32  deg.  fahr. 


25  .977  .994  1.009  1.024  1.040  1.022  1.008  .986 

50  .975  .990  1.005  1.019  1.033  1.017  1.003  .982 

100  .976  .990  1.002  1.014  1.026  1.010     .996  .975 

150  .978  .990  1.000  1.011  1.022  1.007     .992  .969 

250  .982  .991     .999  1.009  1.017  1.003     .986  .962 


.970  .950 

.966  .946 

960  .941 

.955  .938 

.949  .931 


Feed  Water  Temperature  62  deg.  fahr. 


.947  .965  .981  .997  1.013  .996  .983  .963  .948  .930 

.946  .962  .978  .992  1.007  .992  .978  .959  .944  .926 

.948  .961  .974  .988  1.000  .985  .972  .952  .938  .921 

.949  .962  .973  .985     .996  .982  .968  .947  .934  .918 

.954  .964  .972  .983     .992  .979  .963  .940  .928  .912 


Feed  Water  Temperature  92  deg.  fahr. 


25  .917  .936  .953  .970  .987  .971  .958  .939 

50  .917  .933  .950  .965  .980  .966  .954  .936 

100  .919  .933'  .947  .961  .975  .961  .948  .930 

150  .921  .934  .946  .958  .971  .958  .944  .924 

250  .926  .936  .945  .957  .967  .  954  .  940  .919 


.926  .910 

.922  .906 

.917  .902 

.913  .899 

.907  .893 


__  _  Feed  Water  Temperature  122  deg.  fahr. 

25         .888     .907     .924     .942     .960     .945     .933     .916 

50         .887     .905     .922     .938     .954     .941     .929     .913 

100         .890     .905     .920     .935     .949     .936     .924     .907 

150         .892     .906     .919     .932     .945     .933     .920     .902 

250         .897     .909     .918     .931     .941     .930     .916     .897 


.903  .890 

.900  .886 

.895  .882 

.892  .879 

.886  .874 


Feed  Water  Temperature  152  deg.  fahr. 


25  .858  .878  .896  .915  .933  .919  .909  .893 

50  .858  .876  .894  .911  .928  .916  .905  .890 

100  .861  .877  .893  .908  .923  .911  .900  .884 

150  .863  -.879  .892  ,906  .919  .908  .897  .880 

250  .869  .881  .892  .905  .916  .906  .893  .875 


.881  .869 

.879  .866 

.874  .862 

.870  .860 

.866  .855 


Feed  Water  Temperature  182  deg.  fahr. 


25 

.828 

.849 

.868 

.887 

.907 

.894 

50 

.828 

.848 

.867 

.884 

.901 

.890 

100 

.832 

.849 

.865 

.882 

.897 

.884 

150 

.835 

.851 

.865 

.879 

.894 

.883 

250 

.840 

.854 

.865 

.879 

.890 

.881 

.884 

.880     .867 

.876     .862 

.873 

.869 


.857 
.853 


.859  .849 

.857  .846 

.852  .843 

.849  .840 

.845  .836 


_  Feed  Water  Temperature  212  deg.  fahr. 

25         .798     .820     .840     .860     .880     .868     .859     .846 

50         .799     .819     .839     .857     .875     .865     .856     .844 

100         .803     .821     .838     .855     .871     .861     .852     .839 

150         .806     .823     .838     .853     .868     .859     .849     .835 

250         .812     .826     .838     .853     .865     .857     .846     .831 


.837~7829 
.835     .826 
.831     .823 
.828 
.824 


821 
817 


288 


MEASUREMENT      OF      STEAM 


The  steam  as  measured  usually  contains  the  same  per- 
centage of  moisture  or  amount  of  superheat  and  therefore 
the  multiplier  can  be  either  applied  to  the  hourly  coefficient 
for  the  orifice  or  to  the  result. 

Table  57— HORSE  POWER— "POUNDS  FROM  AND 
AT  212  DEG.  FAHR." 


TT                        Pounds 
™£            from  and  at 
212  deg.  fahr. 

Units  of  Evapo- 
ration or  "pounds 
from  and  at 
212  deg.  fahr." 

Horse 
Power 

1 

34.5 

1 

.028986 

2 

69.0 

2 

.057971 

3 

103.5 

3 

.086957 

4 

138.0 

4 

.115942 

5 

172.5 

5 

.144928 

6 

207.0 

6 

.173913 

7 

241.5 

7 

.202899 

8 

276.0 

8 

.231884 

9 

310.5 

9 

.260870 

Due  to  the  fact  that  steam  does  not  accurately  follow  the 
law  of  perfect  gases,  slight  revisions  were  required  for 
various  gauge  pressures,  the  Tables  being  calculated  for  100 
pounds  gauge  pressure. 

It  will  be  noted  in  the  Table  of  Multipliers,  Page  288, 
that  the  percentage  differences  between  the  multipliers  are 
very  small  for  wide  differences  in  the  percentage  of  moisture 
and  quantity  of  superheat.  The  gain  or  loss  in  weight 
per  cubic  foot  and  loss  and  gain  in  heat  content  per  pound 
partially  offset  each  other.  For  this  reason  the  orifice  meter 
is  most  adaptable  for  the  direct  measurement  of  power. 

The  following  examples  illustrate  the  use  of  the  Multipliers 
for  revision  of  Coefficients. 

Example — Steam  being  measured.  Gauge  Pressure,  200 
Ib.  per  square  inch.  Internal  diameter  of  line,  6.065  inches. 
Diameter  of  orifice,  3  inches.  5  per  cent  moisture.  Feed 
Water  Temperature  182  deg.  fahr.  Actual  weight  desired. 

289 


MEASUREMENT      OF      STEAM 

In  Table  53,  Page  282,  the  Coefficient  for  a  6X3  orifice  is 
108.1,  the  Multiplier  for  revision  is  1.011  (Table  54,  Page 
283)  for  200  Ib.  static  pressure  containing  5  per  cent  moisture. 

The  New  Coefficient  =  108.  IX  1.011  =  109.3. 

If  the  power  is  desired  in  Table  55,  Page  287,  the  Co- 
efficient for  a  6X3  orifice  is  129.1,  the  Multiplier  for  200  Ib. 
static  pressure,  feed  water  temperature  182  degrees,  5  per 
cent  moisture  is  .879.  Table  56,  Page  288. 

The  New  Coefficient  =129.  IX.  879  =  113.5. 

Therefore,  a  6X3  orifice  will  pass  113.5  Ib.  of  steam  (from 
and  at  212  deg.  fahr.)  at  a  theoretical  absolute  pressure  of 
1  Ib.  and  at  one  inch  differential  per  hour. 

The  values  of  C,  the  Hourly  Orifice  Coefficient  for  steam, 
contained  in  Tables  53  and  55,  are  prepared  for  pipe  of 
standard  dimensions  (4.026,  6.065,  8.071,  10.191  inches  in- 
ternal diameter)  .  Coefficients  for  pipes  of  other  internal  di- 
mensions can  be  derived  as  follows. 

Example  —  Steam  being  measured. 

Internal  diameter  of  pipe  3.548. 
Diameter  of  Orifice  2J4  inches. 
Actual  Weight  desired. 

2  25 


Cv  for  ratio  .6342  =  .877  (Page  210). 

Coefficient  =  16.36  Cvd2 

=  16.36X.  877X2.25X2.25 
=  72.64  Ib.  of  steam  per  hour. 

The  Multipliers  applicable  to  Table  53  should  be  used 
where  the  pressure  and  quality  of  steam  differ  from  100  Ib. 
gauge  and  saturated  steam. 

290 


MEASUREMENT      OF      STEAM 


I  i 

I 1 

w    •? 


O  si 

P"H  «  JS 

I  II 

2  o 


s.a 

« 


g    §s 
s  = 


8 


!S 


8 


<M  00  1C 


Ci  t>  00  -^        O  O 


b-  O5  i-H  O5 


<M  00  -^ 


Oi 


COOOiO        CO 
t>00(M         t- 


r— I  r— I  CM  Cvj 


8 


O^2  O^ 


O  O  O  O 
O5  <M  CD  T(< 
Tt<  CO  t>  i— i 


l-t   C\J    Tj<    10 


8 


O  O  O 
O5  CM  t- 
(M  T!<  lO 


O  O  ' 


CO  t-  O  O 

OS  "tf  CM   rH 

i— I  OJ  CO 


00  1C  00  O  O 

t-  rH  t>  T*<  rJH 

rH  i-H  <M  OO 


(M<M(MCVJOO 


291 


MEASUREMENT      OF      STEAM 


H    .9 

CO      -g 


§ 


4 


£   . 


rt 

O     S,"S 
£     8| 

J^J      'o   o> 

I" 

3 


O    S 

a  1 


*    o 

c      — . 
«       * 


e 

g 

OS 
0) 

is 

a 

& 

erem 

EH 

$ 

ft 

la 

Y  CAPAC 

iameters  dowi 

s  diameter  of 

50  Inch  Di: 

^ 

T3 

^4 

g 

00 

1 

<u 

% 

^ 

O 

«! 

W 

S 

"o 

O 

U3       » 

• 

<!>      S 

3  ! 

H    -| 
X 

M 

I 
I 


8 


8 


8 


.   <u   tn 

E-  o  <L> 
^^-^ 
rt  -ri  <j 


i-H  i-l  CM        CM 


i-H  r-H        CM  00  lO  CO 


O  O  O  O  ' 
t-  CM  CM  00  ' 


1C  CO  CO  t>  £> 


292 


MEASUREMENT      OF      STEAM 


Table  60 
SIZE  OF  ORIFICES  FOR  MEASURING  STEAM 

Pressures  taken  2^  diameters  upstream  and  8  diameters  downstream. 
Weight  expressed  in  pounds  of  steam  per  hour.    50  inch  Chart. 
Size  of  Meter  is  diameter  of  pipe  line  in  which  orifice  is  placed. 


2  Inch  Meter 

3  Inch  Meter 

4  Inch  Meter 

Pounds 

per 

Gauge  Pressure  Pounds 

Gauge  Pressure  Pounds 

Gauge  Pressure  Pounds 

Hour 

25 

50 

100 

200 

25 

50 

100 

200 

25 

50 

100 

200 

200 

K 

^ 

y% 

K 

N 

7* 

Ys 

K 

K 

M 

8* 

K 

300 

i 

/4 

i 

% 

^8 

i 

K 

N 

400 

iK 

i 

K 

/4 

IK 

1 

K 

%/ 

iK 

i 

K 

600 

1M 

iK 

i 

K 

!3/8 

1/4 

i 

y* 

IN 

IK 

iK 

i  4 

800 

IN 

IK 

iK 

i 

IK 

1^1 

1M 

i 

1^ 

1^ 

iK 

1000 

IK 

IN 

1M 

iK 

1M 

IK 

IN 

iK 

1^4 

1^ 

1^ 

1)4 

1500 

iK 

13/^ 

2 

i^ 

1% 

13/^ 

2 

IK 

IN 

iK 

2000 
3000 

IK 

IK 

2J4 

2M 

2 

1/4 

2 

1^4 

2K 

2K 

1M 

IN 

2 

4000 

2K 

2 

3 

2K 

2K 

6000 

2K 

3 

2^4 

2K 

8000 

3 

gs^ 

10000 

3 

6  Inch  Meter 

8  Inch  Meter 

10  Inch  Meter 

Pounds 

per 

Gauge  Pressure  Pounds 

Gauge  Pressure  Pounds 

Gauge  Pressure  Pounds 

Hour 

i 

25 

50 

100 

200 

25 

50 

100 

200 

25 

50 

100 

200 

400 

IK 

1 

K 

% 

!M 

1 

K 

% 

IK 

1 

K 

^4 

600 

IK 

1/4 

iK 

1 

IK 

iK 

1 

IK 

IK 

i 

800 

IN 

IK 

IK 

1% 

1/4 

iK 

IK 

iK 

IK 

1000 

IK 

iK 

iK 

iK 

i/4 

IK 

ik 

1/4 

IK 

1500 

2  4 

IK 

2K 

2 

1M 

2H 

2 

IN 

IK 

2000 

2K 

2K 

2 

1^4 

2% 

2M 

2 

i^ 

2% 

23^ 

2 

IX 

3000 

3 

2K 

2 

3 

2M 

2K 

2 

3 

2K 

2K 

4000 

3K 

3 

2M 

2//g 

3K 

3 

2/4 

2K 

3K 

3/4 

2J/8 

2//8 

6000 

4 

3K 

3 

2^ 

434 

3/4 

3M 

3 

4J4 

4 

3K 

3 

8000 

4K 

4 

3K 

4K 

4M 

3M 

5 

4K 

4 

3K 

10000 

4K 

4M 

4 

3K 

5 

4K 

4 

3K 

5K 

5 

4K 

3^4 

15000 

4K 

4K 

4 

5K 

5K 

5 

6/4 

5K 

5 

4K 

20000 

4/4 

6 

6 

SK 

4^4 

6/4 

6K 

5% 

5 

30000 

6 

5K 

7K 

6K 

6 

40000 

6 

6K 

60000 

7K 

293 


MEASUREMENT      OF      STEAM 

STEAM  COEFFICIENT  TESTS 

The  following  tests  are  a  portion  of  series  of  tests  which 
were  conducted  at  the  Metric  Metal  Works  several  years 
ago.  The  layout  shown  on  Page  149  was  used,  in  which  a  por- 
tion of  the  steam  from  the  main  header  was  measured  through 
an  orifice  and  subsequently  weighed  as  condensate  by  passing 
the  steam  into  a  barrel  of  cold  water. 

Table  61 


Orifice 

Static 
Pressure 
Ib. 

Differ- 
ential 

Time 
Hr. 

Quan- 
tity 
Ib. 

Coeffi- 
cient 

Remarks 

Pipe  Tap  Connections 


4"x  M" 

103.5 

32.3 

.0766 

22.75 

5.80 

4"x  W 

100.0 

2.3.7 

.0883 

26.75 

5.82 

4"x  %" 

88.0 

39.7 

.0568 

20.5 

5.65 

5.72a 

4"x  Y±" 

95.0 

29.6 

.0723 

23.0 

5.53 

5.75c 

4"x  M" 

99.0 

18.5 

.1231 

32.75 

5.80 

4"x  %» 

105.0 

31.0 

.1078 

37.5 

5.71 

4"x  %* 

102.0 

37.8 

.0874 

33.25 

5.73 

4"x  Yz" 

102.0 

18.5 

.2750 

32.5 

2.54 

4"x  Y2" 

106.0 

20.2 

.2663 

33.5 

2.54 

4"x  W 

110.0 

20.3 

.2687 

35.0 

2.58 

4"x  W 

102.0 

18.8 

.  2713 

32.5 

2.56 

4"x  Y2" 

98.0 

19.4 

.2585 

31.0 

2.57 

2.54a 

4"x  Y2" 

101.0 

21.2 

.2845 

35.25 

2.51 

2.53c 

4"x  W 

96.0 

21.0 

.2833 

34.0 

2.50 

4"x  W 

103.0 

26.0 

.2072 

29.0 

2.53 

4"x  Y2" 

100.0 

3.6 

.5000 

25.0 

2.46 

4"x  W 

101.0 

5.4 

.4525 

29.5 

2.61 

4"x  ^" 

102.0 

22.0 

.2400 

30.5 

2.51 

4"xl" 

98.0 

30.7 

.0605 

37.0 

10.42 

4"xl" 

97.6 

35.0 

.0555 

36.0 

10.35 

10.44a 

4"xl" 

89.8 

21.9 

.0614 

30.5 

10.45 

10.41c 

4"xl" 

107.0 

43.6 

.0415 

30.5 

10.10 

Flange  Connections 


4"xl" 

109.5 

53.0 

.0547 

44.5 

10.04 

4"xl" 

100.0 

42.0 

.0536 

35.75 

9.63 

9.80a 

4"xl" 

110.5 

32.5 

.0702 

44.0 

9.84 

9.90c 

4"xl;/ 

101.5 

43.0 

.0537 

36.75 

9.70 

In  the  column  Remarks,  (a)  refers  to  the  average  value  of  the 
Coefficient  obtained  by  the  tests  and  (c)  is  the  calculated  value  of 
the  Coefficient  obtained  by  assuming  that  the  coefficient  of  velocity 
of  steam  is  the  same  for  steam  as  for  air. 


294 


MEASUREMENT      OF      STEAM 

Preliminary  tests  indicated  a  serious  discrepancy  be- 
tween the  coefficients  as  obtained  by  the  tests  and  the  co- 
efficients as  obtained  by  calculating  the  value  assuming  the 
coefficient  of  velocity  of  steam  the  same  as  the  coefficient  of 
velocity  for  air.  These  discrepancies  were  attributed  to 
condensation  and  after  the  lines  were  thoroughly  insulated 
they  continued  with  the  result  that  the  deviation  was  found 
to  be  due  to  pulsation  as  explained  on  Pages  146  to  151. 

Previous  experiments  by  French  scientists  have  shown  that 
the  flow  of  steam  through  orifices  indicated  that  the  coefficient 
of  velocity  for  steam  and  air  was  the  same. 

In  order  to  verify  the  previous  results,  a  portion  of 
the  tests  were  made  when  there  were  no  reciprocating  units 
connected  with  the  line  and  a  portion  were  conducted 
when  the  reciprocating  units  were  operating.  By  making 
proper  deduction  for  pulsation,  as  indicated  before  and 
after  the  test,  the  results  obtained  compared  favorably  with 
the  results  in  cases  where  the  reciprocating  units  were  not  in 
operation.  As  is  noted  the  duration  of  the  tests  was  very 
limited  and  the  amount  of  condensate  obtained  was  com- 
paratively small.  However,  the  above  results  indicate  that 
the  results  obtained  by  early  experimenters  were  correct. 

In  addition  to  the  above  series  of  tests,  numerous  tests 
have  been  conducted  using  the  orifice  meter  and  differential 
gauge  by  various  refineries  in  which  the  duration  of  the 
tests  lasted  for  several  hours  and  in  which  condensate 
amounted  to  several  hundred  pounds  where  the  percentage 
of  moisture  ranged  from  0  to  15  per  cent.  The  coefficients 
obtained  in  these  tests  ranged  within  1  per  cent  of  the 
published  coefficients,  some  of  them  being  higher  and  some 
lower  and  the  average  deviation  was  less  than  one-half  of 
1  per  cent. 

Some  manufacturers  of  steam  flow  meters  drill  a  small 
opening  in  the  orifice  disc  below  the  orifices,  even  with  the 
level  of  the  lowest  surface  of  the  pipe  when  the  orifice  is 

295 


MEASUREMENT      OF      STEAM 

installed  in  a  horizontal  line.  This  small  opening  is  based 
on  the  theory  that  any  condensate  forming  ahead  of  the 
orifice  will  pass  through  the  small  opening.  Subsequent 
tests  have  indicated  that  such  an  opening  is  entirely  un- 
necessary in  actual  practice,  for  the  reason  that  all  of  the 
moisture  is  carried  through  the  orifice  by  the  steam  and  that 
after  the  orifice  has  been  in  service  a  few  moments  no  moisture 
can  be  obtained  from  a  bleeder  placed  just  ahead  of  the  orifice. 

INSTALLING  AND  TESTING  STEAM  METERS 

See  Pages  303  and  304. 

To  successfully  measure  steam  with  an  orifice  meter 
violent  pulsation  and  vibration  must  be  eliminated. 

The  steam  main  should  be  opened  at  a  flange  connection, 
old  flanges  removed  and  new  flanges  installed.  The  orifice 
disc  is  placed  between  the  flanges  using  sheet  asbestos  gas- 
kets shellaced  to  the  flanges  on  each  side  of  the  orifice  disc. 

When  pressures  are  taken  at  the  flanges  installed  in  a 
horizontal  line,  the  flanges  should  be  set  up  so  that  the  con- 
nections are  on  the  side  or  on  the  top. 

In  drilling  openings  for  connections  where  the  pressures 
are  taken  at  points  2^  diameters  upstream  and  8  diameters 
downstream  from  the  orifice,  the  taps  should  be  on  level  with 
the  center  of  the  pipe  or  on  top  of  the  pipe  if  the  main  is  a 
horizontal  line. 

Connect  the  taps  in  the  main  or  at  the  flanges  with  reser- 
voirs each  constructed  of  either  a  12  inch  length  of  3  inch 
pipe  or  2  feet  of  2  inch  pipe. 

The  tap  in  the  reservoir  should  be  at  the  middle  point  of 
the  reservoir  either  at  the  side  or  in  the  end.  Place  the 
reservoirs  in  a  horizontal  position  level  with  each  other. 
Taps  for  connections  from  the  reservoirs  to  the  gauge  should 
be  in  the  bottom  of  the  reservoirs.  The  pipe  lines  between 
the  reservoirs  and  the  main  line  should  always  drain  toward 
the  main.  The  reservoirs  must  be  at  the  highest  point  in 

296 


MEASUREMENT      OF      STEAM 

the  gauge  line  connection.  Do  not  place  reservoirs  close 
to  the  main  as  it  is  desirable  to  keep  them  cool.  However, 
they  must  be  higher  than  the  gauge. 

Connect  the  reservoir  (attached  to  the  downstream  con- 
nection D  on  the  main),  at  tap  in  the  bottom,  with  gauge 
at  tap  L.  Place  valve  X  in  the  line  adjacent  to  the  gauge. 

Connect  upstream  reservoir,  at  tap  in  the  bottom,  with 
the  gauge  at  tap  H  placing  valve  W  near  the  gauge. 

Install  a  by-pass  placing  valves  at  Z  and  Y  and  a  pet- 
cock  or  valve  at  K. 

The  reservoirs  when  in  operation  will  be  half  filled  with 
water,  level  with  the  connection  from  the  reservoirs  to  the 
main.  The  gauge  lines  from  the  reservoir  to  the  gauge  and 
the  gauge  itself  will  be  filled  with  water  when  in  operation. 
Therefore,  in  order  to  maintain  a  balanced  pressure  on  both 
sides  of  the  gauge  due  to  condensation,  the  reservoirs  must 
be  level  with  each  other  and  higher  than  the  gauge  itself. 
Valves  near  U  and  D  are  auxiliary  valves  used  in  long  lines. 

Setting  up  Gauge,  Glass,  Differential  Pen  Arm, 
Adding  Mercury,  Clock,  Placing  Chart,  Pens  and  Ink, 
Vibrating  Pen  Arm,  and  Adjustments. 

See  the  remarks  contained  under  these  various  headings 
for  measurement  of  gas.  They  apply  for  measurement  of 
steam.  See  Pages  247  to  250. 

Static  Pen  Arm — The  static  pressure  arm  will  rest 
at  a  pressure  equal  to  the  head  of  water  in  the  reservoir  above 
the  elevation  of  the  static  spring  when  there  is  no  pressure 
in  the  main.  Thus,  if  the  reservoirs  are  llj^  feet  above  the 
elevation  of  the  static  spring  the  pen  should  rest  at  5  pounds, 
one  pound  being  equivalent  to  2.3  feet  water  head.  The 
static  pen  can  be  adjusted  to  eliminate  this  difference  by 
setting  on  zero  when  the  gauge,  gauge  lines  and  reservoirs 
are  filled  with  water. 

297 


MEASUREMENT      OF      STEAM 

Turning  on  Steam — Before  turning  steam  pressure  into 
gauge  fill  the  gauge  with  water, 

Open  K,  Y  and  Z 

Then  open  W  and  X  very  slowly  to  admit 
water  to  the  gauge  and  lines  and  release  air 
through  valve  at  K  and  at  funnel. 

Close  X 

After  the  air  is  eliminated  close  funnel 

Close  Y  and  Z 

Open  X 

K  should  be  left  open 

Be  sure  that  valves  Y  and  Z  do  not  leak. 

Orifice  Capacities — After  the  gauge  is  in  operation  if 
the  differential  pen  arm  records  near  the  maximum  reading 
change  the  orifice  to  one  of  a  larger  size.  If  this  is  not  pos- 
sible and  it  is  found  that  the  flow  of  steam  keeps  the  marking 
arm  at  or  above  the  maximum  differential  circle  it  will  be 
necessary  to  use  a  differential  gauge  of  a  higher  range  of 
differential.  If,  after  24  hours,  the  differential  reading  is  at 
or  below  10  per  cent  of  the  maximum  range  of  the  chart  in 
inches,  change  the  orifice  for  one  of  a  smaller  size  or  use  a 
differential  gauge  with  a  smaller  maximum  range.  For 
Orifice  Capacities  see  Pages  291  and  292. 

Checking  Differential  Gauge  for  Zero  :— 

Open  Y  slightly  until  water  flows  from  K 

Close  K 

Close  W  and  X 

Open  Y  and  Z,  then  open  K 

The  differential  pen  arm  should  return  to  zero. 

Buoyancy  of  Float — The  zero  position  of  the  pen  arm 
in  a  gauge  filled  with  water  is  not  the  same  as  when  filled 
with  air  due  to  the  increased  buoyancy  of  the  float  on  account 
of  the  water. 

298 


MEASUREMENT      OF      STEAM 


Fig.   119— DIFFERENTIAL  GAUGE  WHICH  INDICATES  RATE  OF 
FLOW  PER  HOUR.     SEE  PAGES  130  AND  131. 
Patent  applied  for 


299 


MEASUREMENT      OF      STEAM 

Zero  Float  Position — The  differential  pen  arm  should  be 
kept  in  a  straight  line  at,  the  flexible  joint.  The  differential 
pen  arm  can^be  adjusted  to  zero  by  moving  slightly  at  the 
flexible  joint  or  at  the  connection  with  the  shaft.  When  the 
pen  arm  rests  at  zero  determine  if  the  float  is  floating  and 
not  resting  on  the  bottom  of  the  mercury  pot. 
Partially  close  Y 

Open  X  carefully  when  the  differential  pen 
should  recede  one-fourth  inch  or  more  (actual 
measurement)  below  the  zero  line.  If  the  float 
rests  on  the  bottom  of  the  chamber  at  zero  add 
mercury.  See  paragraph  Adding  Mercury, 
Page  247. 

After  test,  close  X 
Open  Y 

Checking  Differential  Pen  Arm — 

Close  W  and  X 

Attach  a  single  column  glass  tube  with  a 
rubber  connection  and  nipple  to  tap  at  P  and 
fasten  tube  in  a  rigid  vertical  position.  See 
Figs.  120  and  121  for  examples. 

Open  K,  Y  and  Z 

Open  W  and  admit  water  slowly  to  expel  air 
fromK 

Mark  level  of  water  in  glass  tube  attached  to 
connection  at  P 

Close  Z 

By  partially  opening  and  closing  W  the  reading 
can  be  checked  with  the  column  of  water  in  the  tube  above 
the  zero  mark.  One  inch  of  water  reading  on  the  chart  is 
equal  to  0.926  inches  of  water  head  in  the  glass  column 
above  the  zero  position.  The  following  Table  indicates  the 
various  check  readings. 

300 


MEASUREMENT      OF      STEAM 

Table  62— CHECK  READINGS  FOR  DIFFERENTIAL 
GAUGE  FILLED  WITH  WATER 


Differential 

Water  Column 

Differential        Water  Column 

Gauge  Reading 

Head 

Gauge  Reading              Head 

Inches 

Inches 

Inches                   Inches 

1 

.93 

10 

9.3 

2 

1.85 

20 

18.5 

3 

2.77 

30 

27.7 

4 

3.71 

40 

37.1 

5 

4.63 

50 

46.3 

6 

5.56 

60 

55.6 

7 

6.49 

70 

64.9 

8 

7.41 

80 

74.1 

9 

8.34 

90 

83.4 

100                          926 

After  Test,  open  Z,  close  P,  then  proceed  as  in  Turning 
on  Steam,  Page  298. 

The  differential  pen  arm  may  be  tested  as  in  testing 
with  gas  if  the  water  is  removed  from  the  gauge  and  air 
pressure  is  used. 


Fig.   120  Fig.  121 

Showing  typical  methods  of  '  attaching  tube  for  water  column 
test.  Points  K  and  P  may  be  located  at  other  openings  as  shown  in 
the  various  installations. 


301 


MEASUREMENT      OF      STEAM 

Testing  Static  Spring — To  test  the  static  pressure  gauge, 
attach  the  test  gauge  at  G,  and  check  the  two  gauges. 

If  the  static  spring  is  adjusted  for  head  of  water  in  gauge 
lines  and  reservoirs  above  the  gauge,  in  testing,  the  adjust- 
ment should  be  added  to  the  static  pressure  arm  reading  to 
check  with  the  test  gauge.  See  same  subject,  Page  258. 

Leaks — Watch  all  connections  for  leaks.  There  should 
be  no  leaks  at  any  connection.  Special  attention  should 
be  given  to  valve  stems  for  leakage. 

General — Before  turning  the  pressure  into  the  gauge, 
always  make  sure  valves  W  and  X  are  closed  before 
opening  valves  Y  and  Z  or  either  Y  or  Z.  This  precaution 
will  eliminate  the  circulation  of  water  through  the  by-pass, 
and  heating  of  the  gauge  lines. 


Fig.  122—400  INCH  GAUGE  USED  FOR  TESTING  PURPOSES 


302 


MEASUREMENT      OF      STEAM 


Upstream  Connection  Downstream  Connection 


'  Sect/on  M-M 


Jest  Conn  e> 


Mart 

X 

Test  Connect /on 

•Differential  Pressure  Gauge 
ryDram 


Fig.  123—50  INCH  GAUGE  INSTALLATION  FOR  MEASURING  STEAM 


303 


MEASUREMENT      OF      STEAM 


Upstream  Connection 
J- — ffeserw/rs- 


Test  Connection 

Different/a/ 
Pressure  fa upe 


tinnect/o/? 

'era/ft/ Drain 
Cnort 


Fig.l24—50or  100  INCH  GAUGE  INSTALLATION  FOR 
MEASURING  STEAM 


304 


MEASUREMENT      OF      STEAM 

READING  CHARTS 

The  formula  for  use  in  measuring  steam  with  the  orifice 
meter  is 

Quantity  =  C 


C  =  Coefficient  obtained  from  Table  of  Coefficients 
or  calculated   for  the  proper   size  of    orifice, 
diameter  of  pipe,  quality  and  pressure. 
h  =  differential  pressure  in  inches  of  water. 
A  —atmospheric  pressure  in  Ib.  per  square  inch. 
p  =  static  pressure  expressed  in  Ib.  per  square  inch. 
To  simplify  all  calculations,  Tables  of  Pressure  Extensions 
have  been  published  which  give  the  results  of  the  formula 


in  figures  for  various  combinations  of  pressure  and  differential 
readings  from  29  inches  vacuum  to  500  Ib.  pressure  and  from 
1  inch  to  100  inches  differential.  This  eliminates  the  ne- 
cessity of  figuring  out  the  formula  for  each  reading  in  deter- 
mining the  volume  of  steam  passing  the  meter.  In  this 
formula,  the  atmospheric  pressure  is  assumed  as  14.4  Ib. 
Adjustment  must  be  made  to  the  static  pen  arm,  or  to  the 
static  pressure  readings  as  explained  on  Page  297,  on 
account  of  the  elevation  of  the  reservoirs  above  the  gauge. 

To  obtain  the  quantity  passing  the  meter,  average  the 
differential  pressure  (marked  in  red  ink)  and  the  static  pres- 
sure (marked  in  black  ink)  on  the  chart  for  each  hour. 

If  the  differential  pressure  varies  over  wide  ranges  during 
the  daily  period,  the  method  used  for  gas  should  be  applied. 

As  the  static  pressure  is  usually  fairly  constant,  average 
the  differential  reading  for  the  day  and  the  static  reading  for 
the  day.  The  pressure  extension  is  obtained  for  the  average 
readings  and  is  multiplied  by  the  number  of  hours  for  which 
the  average  was  obtained.  This  product  is  then  multiplied 
by  the  Hourly  Orifice  Coefficient. 

305 


MEASUREMENT      OF      STEAM 

Frequently  a  planimeter  and  reference  chart  is  used  to 
obtain  the  average  differential  reading  and  average  static 
reading.  This  method  eliminates  the  necessity  of  recording 
the  differential  and  static  pressures  on  the  chart  and  greatly 
simplifies  the  work.  It  should  only  be  used  when  the  static 
pressures  or  differential  pressures  do  not  vary  over  wide 
limits,  as  the  results  in  such  cases  will  be  greater  than  the  true 
result. 

The  pressure  carried  in  steam  lines  does  not  usually  vary 
over  wide  ranges,  and  quite  frequently  is  almost  constant. 
Due  to  this  fact,  the  static  pressure  is  not  recorded  by  some 
makes  of  flow  meters,  thus  these  meters  have  a  semblance 
of  simplicity  which  does  not  really  exist.  Meters  which 
record  the  static  pressure  as  well  as  the  differential  pressure 
give  the  operator  an  accurate  report  of  the  condition  at  the 
meter. 

When  the  static  or  line  pressure  is  constant  the  work  in- 
volved in  obtaining  the  flow  is  greatly  simplified.  The  form- 
ula C-\/  hP  can  be  reduced  to  Cs  V  h  in  which  Cs  is  equal  to 
C  VP»  P  being  the  pressure  extension  for  one  inch  differential. 
This  steam  Coefficient  Cs  is  used  as  a  multiplier  for  the  sum 
of  the  hourly  values  of  V~&  (Page  313). 

Example — 

Line  Pressure,  100  Ib. 
Pipe  Diameter,  4  inches. 
Orifice  Diameter,  2J/£  inches. 
C  =  87.76       (Page  282) 
Cs  =  87.76  V  100+14.4 
-87.76X10.696  =  938.7 

This  Steam  Coefficient  is  also  used  as  the  multiplier  for  the 
average  differential  reading  obtained  by  using  a  planimeter 
and  multiplying  by  24. 

All  Orifice  meter  chart  calculations  are  simplified  by  the 
use  of  the  Orifice  Meter  Calculator,  Page  267. 

306 


PART  SIX 

MEASUREMENT  OF  WATER. 

The  type  of  meter  and  gauge  used  for  measuring  water 
is  identical  with  that  used  for  measuring  gas  or  air,  with 
the  exception  that  the  static  pressure  spring  may  be  omitted 
as  water  and  oil  are  practically  incompressible.  The  same 
types  of  charts  are  used,  reducing  to  a  minimum  the  various 
styles  and  amounts  of  supplies  required,  not  to  mention  the 
decrease  of  maintenance  and  inspection.  The  operator 
needs  to  be  familiar  with  only  one  type  of  meter  and  the  office 
work  is  greatly  simplified  as  only  one  kind  of  chart  is  to  be 
read. 

The  measurement  of  water  by  the  orifice  meter  is  greatly 
simplified  due  to  absence  of  all  multipliers  for  revision  of 
coefficients. 

For  each  installation  the  orifice  in  the  orifice  disc,  when 
placed  in  the  pipe  line,  forms  a  definite  section  of  unchanging 
area,  and  creates  a  definite  difference  between  the  static 
pressure  of  the  fluid  on  the  upstream  side  of  the  orifice,  and 
the  static  pressure  of  the  fluid  on  the  downstream  side  of 
the  orifice,  for  each  velocity  or  rate  of  flow  of  the  fluid,  at 
the  same  density.  This  difference  in  static  pressures  is 
termed  the  differential  pressure  or  the  "differential."  In 
other  words  the  "differential,"  in  cases  of  liquids,  indicates 
the  velocity. 

The  Differential  Gauge  records  on  a  chart  the  differential 
pressure  existing  between  the  pressure  connections.  This 
factor  with  the  known  area  of  the  orifice  enables  us  to  de- 
termine the  flow  from  the  formula: 


307 


MEASUREMENT      OF      WATER 

Where  ()  =  the  Quantity  of  liquid  passing  the 
orifice.  The  result  can  be  expressed  in 
"gallons"  or  "barrels"  per  hour. 

C  =  the  Hourly  Coefficient.  The  value  of  this 
term  remains  the  same  for  each  installation 
and  basis  of  measurement. 

h  =  the  Differential  Pressure  existing  between  the 
two  pressure  connections,  expressed  in  inches 
of  water  head,  this  value  is  recorded  graphi- 
cally on  the  chart  of  the  Recording  Dif- 
ferential Gauge. 

The  value  of  the  Hourly  Orifice  Coefficient  C  in  the 
above  formula  is  found  on  Page  312,  computed  for 
various  diameters  of  orifice  and  diameters  of  pipe,  these 
values  having  been  determined  by  exhaustive  experimental 
and  practical  tests  in  comparison  with  actual  displacement. 
The  extensions  of  the  values  of  V  h  have  been  compiled  and 
are  given  in  Table  64. 

Example — One  hour  reading  (water  being  measured) : 
Average  differential  reading  h  =  25  inches. 
Diameter  of  Pipe=  4  inches. 
Diameter  of  Orifice  =  2  inches. 

Hourly  Orifice  Coefficient  C  =  963.1  for  2  inch  orifice  in  a 
4  inch  line  (Page  312). 

Quantity  per  hour,  Q  =  963.1   V25 

Orifice  Pressure 

=   963.1    X     5.000  =  4816  gallons. 

Coefficient          Extension. 

Therefore  the  quantity  per  hour  flowing  in  the  line  is 
equal  to  the  Orifice  Coefficient  multiplied  by  the  Differential. 

308 


MEASUREMENT      OF      WATER 

The  relation  between  the  differential  and  the  velocity  of 
the  fluid  through  the  orifice  is  expressed  by  the  formula: 


Where  V '  —  velocity  of  flowing  fluid  in  feet  per  second. 

g  =  acceleration  due  to  gravity  in  feet  per  sec.,  per 
sec. -32.16. 

H  =  differential  expressed  in  feet  head  of  flowing 
fluid. 

The  well  known  formula  V=  ^j2gH  expresses  the  theo- 
retical flow  eliminating  friction  and  other  influences.  When 
applied  to  actual  conditions  a  correcting  factor  is  used  to 
take  care  of  influences  due  to  contraction  of  jet,  friction,  etc. 
This  correcting  factor  Cv  is  commonly  known  as  the  "co- 
efficient of  velocity." 

In  this  formula  the  differential  head  is  expressed  in  feet 
head  of  flowing  fluid : 


Where  H  =  differential  in  feet  head  of  flowing  fluid. 

h  =  differential  in  inches  of  water  pressure. 
12  =  number  of  inches  in  a  foot. 
Substituting  the  value  of  H  in  formula    V  =  C 


Weobtain  F= 


=  2.31520 


In  measuring  water  with  an  orifice  meter  the  connecting 
lines  and  the  gauge  itself  are  filled  with  water,  thus  the  heads 
of  liquid  acting  on  each  portion  of  the  gauge  are  equal. 

309 


MEASUREMENT      OF      WATER 

Due  to  the  fact  that  the  recording  gauges  are  filled  with 
water  each  inch  of  mercury  differential  is  partially  counter- 
balanced by  an  inch  of  water.  Each  inch  of  mercury  dif- 
ferential is  equivalent  to  only  (13.6 — 1.0)  inches  of  water 
differential  instead  of  13.6  inches  which  would  be  the  case  if 
the  water  did  not  fill  the  gauge  and  connections. 

Where  13. 6  =  specific  gravity  of  mercury. 

1.0  =  specific  gravity  of  water  in  gauge. 

Therefore,  the  differential  h  is  multiplied  by  the  factor 
12.6/13.6  for  the  reason  that  differential  gauges  are  con- 
structed to  indicate  13.6  inches  of  water  pressure  differential 
for  each  inch  of  mercury  differential. 

Substituting  these  factors  in 

V  =  2.3152  C,VT 
we  obtain 

12.6ft 


13.6 

The  quantity  of  water  passing  the  orifice  in  gallons  per 
hour  is  equal  to  the  area  of  the  orifice  in  square  inches  multi- 
plied by  the  velocity  in  inches  per  hour  divided  by  231.  This 
fact  may  be  expressed  by  the  following  formula  : 

0.7854  d2 
Q=  — — X3600XFX12 

ZoL 

<2  =  146.88  <22XF 

Wrhere  Q  =  quantity  of  water  passing  the  orifice  in  gallons 
per  hour. 

0.7854  d2  =  area  of  orifice  in  square  inches. 

d  =  diameter  of  orifice  in  inches. 

231  =  number  of  cubic  inches  in  a  gallon. 

3600  =  seconds  in  one  hour. 

F  =  velocity  of  water  through  orifice  in  feet  per  sec. 

12  =  number  of  inches  in  a  foot. 

310 


MEASUREMENT      OF      WATER 

Substituting  the  value  of  V  where  7  =  2.2284  Cv  ^~h 
in  this  expression. 

Q=  146.88^2X2.2284C,Vl 
Q  =  327.31  C^2V"A  =  CV"A 

The  Hourly  Coefficient  C  in  Table  63  is  equal  to 
327.31  Cvd2. 

It  has  been  found  that  the  simple  layout  shown  in  Figs. 
125  and  126  can  be  used  very  satisfactorily  for  measuring 
light  oils  or  oils  of  low  viscosity,  see  Part  7. 

The  values  of  C,  the  Hourly  Orifice  Coefficients  for  Water, 
are  given  in  Table  63.  These  Coefficients  are  prepared  for 
pipe  of  standard  dimensions  (2.067,  3.068,  4.026,  6.065,  8.071 
and  10.191  inches  internal  diameter).  Coefficients  for  pipes 
of  other  internal  diameters  for  various  sizes  of  orifices  can  be 
calculated  as  follows. 

Example  —  Water  being  measured. 

Internal  Diameter  of  Pipe  7.981  inches. 
Diameter  of  Orifice  4  inches. 


Ratio  X  =  .  5012 

7.981 

Cv  for  ratio  .5012  =  .739  (Page  209). 

Coefficient  =327.31Qf 

=  327.31  X.  739  X4X4 
=  3870  gallons  per  hour. 


311 


MEASUREMENT      OF      WATER 


Table  63 
HOURLY  ORIFICE  COEFFICIENTS  FOR  WATER 

Pressures  taken  2J/£  diameters  upstream  and  8  diameters  downstream. 

Values  of    C  in  Q  =  C  V  h       where    Q  expresses  the  quantity  of    water  passing 

through  the  orifice  in  gallons  per  hour. 
Size  of  Meter  is  the  diameter  of  pipe  line  in  which  orifice  is  placed. 


Diam. 
of 


DIAMETER  OF  PIPE  LINE 


unnce 
Inches 

2" 

3" 

4" 

6* 

8" 

10" 

y* 

5A 
H 

7A 

51.69 
82.42 
122.1 

172  8 

50.68 
79.96 
116.4 
160  5 

50.22 
79.04 
114.7 
157  3 

113^0 

1 

iy<. 

237.7 
321  2 

213.1 
275  3 

207.2 
264  8 

202.8 

200.9 

IK 

i*A 

« 

m 

1% 

IK 

2 

21A 

429.3 
569.7 
752.2 

348.6 
435.2 
537.5 
658.8 
802.9 
974.9 
1180. 
1424 

330.7 
405.8 
491.1 
587.7 
697.3 
821.6 
963.1 
1124 

320.0 
466  0 
642*8 
853.7 

316.1 
458.6 
628~9 
'828^5 

313.8 
454^5 
622^  i 
817!2 

2X 
2% 

1716. 

1308. 
1518 

1104. 

1059. 

1041. 

21A 
2% 
2% 

2ys 

3 

&A 

ay2 

&A 

4 

4M 

V/2 

&A 

5 

5K 

1758. 
2033. 
2347. 
2707. 
3118. 

1399. 
1749  ! 

2162  !' 
2654. 
3240. 
3940. 

4777. 
5776. 
6973. 

1323. 
1623  ! 

1963  ! 
2349. 

2787. 
3283. 
3848. 
4491. 
5224. 
6060. 
7017. 
8112 

1294. 
1577!  ' 

1893  '.' 
2244. 
2632. 
3061. 
3535. 
4057. 
4636. 
5275. 
5982. 
6766. 

5U 

9364 

7635. 

5M 

10800  . 

8600. 

6 

12430  . 

9674. 

6M 

10870. 

Q1A 

12190. 

6% 

13670. 

7 

15310  . 

7M 

17130. 

7^ 

19160. 

312 


MEASUREMENT      OF      WATER 


Table  64 
DIFFERENTIAL  PRESSURE  EXTENSIONS 

Values  of  V7T  from  1  to  100  Inches 


Differential 
Reading 
h  Inches 

Extension 

VT 

Differential 
Reading 
h  Inches 

Extension 

VT 

Differential 
Reading 
h  Inches 

Extension 

VT 

1.0 

l.COO 

8.4 

2.898 

45 

6.708 

1.1 

1.049 

8.6 

2.933 

46 

6.782 

1.2 

1.095 

8.8 

2.966 

47 

6.856 

1.3 

1.140 

9.0 

3.000 

48 

6.928 

1.4 

1.183 

9.2 

3.033 

49 

7.000 

1.5 

1.225 

9.4 

3.066 

50 

7.071 

1.6 

1.265 

9.6 

3.098 

51 

7.141 

1.7 

1.304 

9.8 

3.130 

52 

7.211 

1.8 

1.342 

10.0 

3.162 

53 

7.280 

1.9 

1.378 

10.2 

3.194 

54 

7.348 

2.0 

1.414 

10.4 

3.225 

55 

7.416 

2.1 

1.449 

10.6 

3.256 

56 

7.483 

2.2 

1.483 

10.8 

3.286 

57 

7.550 

2.3 

1.517 

11.0 

3.317 

58 

7.616 

2.4: 

1.549 

11.5 

3.391 

59 

7.681 

2.5 

1.581 

12. 

3.464 

60 

7.746 

2.6 

1.612 

12.5 

3.536 

61 

7.810 

2.7 

1.643 

13. 

3.606 

62 

7.874 

2.8 

1.673 

13.5 

3.674 

63 

7.937 

2.9 

1.703 

14. 

3.742 

64 

8.000 

3.0 

1.732 

14.5 

3.808 

65 

8.062 

3.1 

1.761 

15. 

3.873 

66 

8.124 

3.2 

1.789 

15.5 

3.937 

67 

8.185 

3.3 

1.817 

16. 

4.000 

68 

8.246 

3.4 

1.844 

16.5 

4.062 

69 

8.307 

3.5 

1.871 

17. 

4.123 

70 

8.367 

3.6 

1.897 

17.5 

4.183 

71 

8.426 

3.7 

1.924 

18. 

4.243 

72 

8.485 

3.8 

1.949 

18.5 

4.301 

73 

8.544 

3.9 

1.975 

19. 

4.359 

74 

8.602 

4.0 

2.000 

19.5 

4.416 

75 

8.660 

4.1 

2.025 

20. 

4.472 

76 

8.718 

4.2 

2.049 

20.5 

4.528 

77 

8.775 

4.3 

2.074 

21 

4.583 

78 

8.832 

4.4 

2.098 

22 

4.690 

79 

8.888 

4.5 

2.121 

23 

4.796 

80 

8.944 

4.6 

2.145 

24 

4.899 

81 

9.000 

4.7 

2.168 

25 

5.000 

82 

9.055 

4.8 

2.191 

26 

5.099 

83 

9.110 

4.9 

2.214 

27 

5.196 

84 

9.165 

5.0 

2.236 

28 

5.292 

85 

9.220 

5.2 

2.280 

29 

5.385 

86 

9.274 

5.4 

2.324 

30 

5.477 

87 

9.327 

5.6 

2.366 

31 

5.568 

88 

9.381 

5.8 

2.408 

32 

5.657 

89 

9.434 

6.0 

2.449 

33 

5.745 

90 

9.487 

6.2 

2.490 

34 

5.831 

91 

9.539 

6.4 

2.530 

35 

5.916 

92 

9.592 

6.6 

2.569 

36 

6.000 

93 

9.644 

6.8 

2.608 

37 

6.083 

94 

9.695 

7.0 

2.646 

38 

6.164 

95 

9.747 

7.2 

2.683 

39 

6.245 

96 

9.798 

7.4 

2.720 

40 

6.325 

97 

9.849 

7.6 

2.757 

41 

6.403 

98 

9.899 

7.8 

2.793 

42 

6.481 

99 

9.950 

8.0 

2.828 

43 

6.557 

100 

10.000 

8.2 

2.864 

44 

6.633 

313 


MEASUREMENT      OF      WATER 


Table  65 
HOURLY  CAPACITIES  OF  ORIFICES  FOR  WATER 

Pressures  taken  23^  Diameters  Upstream  and  8  Diameters  Downstream. 

Capacities  expressed  in  Gallons. 
Size  of  Meter  is  the  Diameter  of  Pipe  Line  in  which  Orifice  is  placed . 

50  Inch  Differential  Chart 


Orifice 
Diam. 
Inches 

Size  of  Meter 

Orifice 
Diam. 
Inches 

Size  of  Meter 

2" 

3" 

4" 

6" 

8" 

10" 

Vi 

232 

227 

225 

11A 

1430 

1410 

1400 

« 

370 

358 

353 

11A 

2090 

2050 

2030 

% 

550 

520 

510 

IX 

2880 

2810 

2780 

7/i 

780 

720 

700 

2 

3830 

3710 

3670 

1080 

960 

930 

2Y2 

6300 

5900 

5800 

ly* 

1460 

1230 

1190 

3 

9700 

8800 

8500 

1M 

1960 

1570 

1480 

&A 

14500 

12500 

11800 

m 

2620 

1950 

1820 

4 

21400 

17200 

15800 

IH 

3460 

2420 

2200 

&A 

31100 

233CO 

20800 

IK 

3620 

3130 

5 

31300 

26800 

2 

5370 

4320 

5^ 

42000 

34200 

*1A 

7800 

5860 

6 

56000 

43000 

&A 

7900 

6^ 

55000 

2% 

10500 

7 

68000 

3 

14000 

VA 

86000 

100  Inch  Differential  Chart 


Orifice 
Diam. 
Inches 

Size  of  Meter 

Orifice 
Diam. 
Inches 

Size  of  Meter 

2" 

3" 

4" 

6" 

8" 

10" 

1A 

328 

320 

318 

1M 

2020 

2000 

2000 

Ys 

520 

510 

500 

IH 

2950 

2900 

2880 

H 

780 

740 

730 

i*A 

4080 

3980 

3940 

7/8 

1100 

1020 

990 

2 

5400 

5300 

5200 

1520 

1350 

1310 

21A 

8900 

8400 

8200 

V/8 

2070 

1750 

1680 

3 

13700 

12500 

12000 

1M 

2780 

2220 

2100 

3^ 

20500 

17700 

16700 

iy» 

3700 

2770 

2570 

4 

30200 

24400 

22400 

IH 

4900 

3420 

3110 

&A 

44000 

33000 

29400 

m 

5100 

4420 

5 

44300 

37000 

2 

7600 

6100 

5^ 

59000 

48000 

2^ 

11000 

8300 

6 

79000 

61000 

2y2 

11100 

Q1A 

77000 

2% 

14900 

7 

97000 

3- 

19700 

VA 

122000 

For  Minimum  Capacity  deduct  50  per  cent.,  and  for  Maximum 
Capacity  add  50  per  cent. 

314 


MEASUREMENT      OF      WATER 


WATER  COEFFICIENT  TESTS 

In  the  following  tests,  a  refers  to  the  average  value  of 
the  coefficient  as  obtained  by  the  test.  The  calculated 
coefficient  c,  is  the  coefficient  which  was  obtained  by 
assuming  that  the  "coefficient  of  velocity"  for  water  was 
the  same  as  the  "coefficient  of  velocity"  for  air,  the  actual 
internal  diameter  of  pipe  being  used  in  all  instances.  The 
results  of  the  above  tests  substantiate  the  fact  that  the  co- 
efficient of  velocity  for  air  can  be  used  as  the  coefficient  of 
velocity  for  water  in  orifice  meter  computations. 

Table  66 


Orifice 

Differ- 
ential 
Inches 

Time 
vSeconds 

Quan- 
tity 
Gallons 

Coeffi- 
cient 

Remarks 

Pressures  taken  2}/£  diameters  upstream  and  8  diameters  downstream 


2"x  }/2" 

34.2 

373 

31.5 

52.0 

51.  8a 

2"x  Y2" 

44.5 

330 

31.5 

51.6 

51.  8c 

2"x  %" 

38.0 

148 

31.5 

124.5 

2"x  %" 

37.0 

149 

31.5 

125.2 

2"x  %* 

36.0 

150.5 

31.5 

125.5 

125.  Oa 

2"x  %" 

50.0 

128.5 

31.5 

124.7 

123.  Oc 

2"xl" 

30.0 

85.8 

31.5 

241.5 

242.  Oa 

2"xl" 

20.0 

105.5 

31.5 

240.2 

240.  5c 

2"xl" 

11.0 

140.0 

31.5 

244.0 

4"xl" 

48.0 

666.5 

262.3 

205. 

205.  Oa 

4"xl'/ 

35.0 

770.0 

259.0 

205. 

207.  2c 

4"xlM" 

36.0 

221.5 

253.0 

686. 

4"xl34" 

23.0 

271.0 

256.5 

713. 

4"xl%" 

41.5 

209.0 

261.0 

698. 

700.  Oa 

4"xlM" 

30.5 

241.5 

260.0 

702. 

697.  3c 

4"xW 

42.0 

206.5 

259.0 

697. 

4"xl%" 

23.0 

279.0 

261.0 

704. 

Pressures  taken  at  Flange 


2"x  %" 

2"x  %" 

44.0 
32.0 

153.0 

178.5 

31.5 
31.5 

111.8 
112.3 

112.  la 
lll.Sc 

4"xl" 
4"xl" 

46.5 
48.0 

715.5 
680.0 

262.3 
256.5 

194. 
196. 

195.  Oa 
198.  Oc 

4"xl%" 

4"xl%" 

52.0 
29.0 

212.0 
277.0 

259.0 
255.5 

610. 
616. 

613.  Oa 
609.  Oc 

315 


MEASUREMENT      OF      WATER 

INSTALLING  AND  TESTING  WATER  METERS 

The  preceding  instructions  relative  to  gas:  Measuring 
Gases  and  Liquids,  Orifice  Meter  Body,  Orifice  Meter 
Flanges,  Gauge  Line  Connections  or  Taps,  Setting  up  Gauge, 
Differential  Pen  Arm,  Glass,  Adding  Mercury,  Static  Pres- 
sure Connections,  (Pages  239  to  248)  apply  for  measuring 
water  with  the  following  exceptions :  In  measuring  water  the 
installation  may  be  made  in  any  line  whether  level,  inclined 
or  vertical.  The  main  line  by-pass  and  valves  may  be 
omitted. 

By  Pass — Install  by-pass,  placing  valve  at  Z. 
Removing  Chart,  Clock,  Placing  Chart,  Pens  and  Ink, 
Vibrating  Pen  Arm,  and  Adjustments  (Pages  248-250,  258)— 
These  articles  apply  with  the  exception  that  the  static  spring 
and  pen  arm  are  not  necessary  for  measurement  as  these 
liquids  are  practically  incompressible. 
Starting  Gauge — Fill  gauge  with  water. 
Open  Z,  K  and  P 

Open  valve  W  slightly  to  admit  line  pressure 
eliminating  air  at  K  and  P.  Open  and  close 
funnel  to  release  all  of  the  air.  When  all  air  is 
eliminated, 

Close  P  and  K 
Open  W 
Close  Z 
OpenX 

Leaks — Stop  all  leaks. 

Orifice  Capacities — See  Page  298.  Same  subject,  these 
instructions  apply  for  water  as  well  as  for  steam.  For  cap- 
acities see  Page  314. 

Checking  Differential  Gauge  for  Zero — 
Close  W  and  X 
Open  K       Open  Z 
The  differential  pen  should  return  to  zero. 

316 


MEASUREMENT      OF      WATER 

The  differential  pen  arm  should  be  kept  in  a  straight  line. 
It  can  be  adjusted  to  zero  by  moving  slightly  at  the  joint  or  at 
the  connection  with  the  shaft.     When  the  pen  rests  at  zero, 
determine   if  the  float  is  floating  and  not  resting  on  the 
bottom  of  the  chamber.     See  Buoyancy  of  Float,  Page  298. 
Close  Z  and  K 
Partially  open  P 

Then  open  X  carefully  when  the  differential 
pen  should  recede  one-fourth  inch  or  more  (actual 
measurement)  below  the  zero  line.     If  the  float 
rests  on  the  bottom  of  the  chamber  at  zero,  add 
mercury.     (See  Adding  Mercury.)      Page  247. 
After  test  close  P  and  X 
OpenZ 

Checking  Differential  Pen  Arm — 

Close  W  and  X 

Attach  a  single  column  glass  tube  with  a 
rubber  connection  and  nipple  at  tap  P  and  fasten 
tube  in  a  rigid  vertical  position.  Page  301. 

Open  K  and  Z 

Open  W  slightly  and  admit  pressure  slowly  to 
expel  air  from  K 

Mark  level  of  water  in  glass  tube  attached  to 
connection  at  P. 

Close  Z 

By  opening  and  closing  W  the  reading  can  be 
checked  with  the  column  of  water  in  the  tube 
above  the  zero  mark.  One  inch  of  differential 
reading  on  the  chart  being  equal  to  0.926  inches 
of  water  head  in  the  water  column.  See  Table 
Page  301. 

Reading    Charts— See    Page  340.      These    instructions, 
relative  to  Reading  Charts,  apply  to  the  water  measurement. 

317 


MEASUREMENT      OF      WATER 


—Zg  Diameters 


Fig.  125—50  INCH  GAUGE    INSTALLATION  FOR   MEASURING    WATER 
OR  LIGHT  OILS.     FLANGE  CONNECTIONS  SHOWN  DOTTED 


Fig.  126—50  OR  100  INCH     GAUGE  INSTALLATION    FOR     MEASURING 
WATER  OR  LIGHT  OILS.     FLANGE  CONNECTIONS  SHOWN  DOTTED 

318 


PART    SEVEN 

MEASUREMENT  OF 


The  Orifice  Meter  in  combination  with  the  Differential 
Gauge  was  designed  primarily  to  measure  gases  under  high 
pressure.  During  the  past  few  years  they  have  been  used 
successfully  for  measuring  many  kinds  of  liquids,  such  as 
gasoline,  kerosene,  crude  oil,  and  reduced  Mexican  crude 
oil. 

The  type  of  meter  and  gauge  used  for  measuring  oil  is 
identical  with  that  used  for  measuring  gas  or  air,  with  the 
exception  that  the  static  pressure  spring  may  be  omitted  as 
water  and  oil  are  practically  incompressible.  The  same 
types  of  charts  are  used,  reducing  to  a  minimum  the  various 
styles  and  amounts  of  supplies  required,  not  to  mention 
the  decrease  of  maintenance  and  inspection.  The  operator 
needs  to  be  familiar  with  only  one  type  of  meter  and  the 
office  work  is  greatly  simplified  as  only  one  kind  of  chart  is 
to  be  read. 

The  meter  is  installed  in  the  same  manner  as  for  measur- 
ing gas.  Simply  place  an  orifice  in  an  orifice  meter  body  or 
between  two  flanges  in  an  existing  line,  making  two  small 
pipe  pressure  connections  leading  from  the  pipe  line,  one  on 
each  side  of  the  orifice,  to  the  differential  gauge.  The  gauge 
may  be  installed  at  any  location  convenient  for  observation 
and  inspection. 

For  each  installation  the  orifice,  in  the  orifice  disc,  when 
placed  in  the  pipe  line,  forms  a  definite  section  of  unchanging 
area,  and  creates  a  definite  difference  between  the  static 

319 


MEASUREMENT      OF      OIL 


pressure  of  the  fluid  on  the  upstream  side  of  the  orifice,  arid 
the  static  pressure  of  the  fluid  on  the  downstream  side  of 
the  orifice,  for  each  velocity  or  rate  of  flow  of  the  fluid,  at 
the  same  density.  This  difference  in  static  pressures  is 
termed  the  differential  pressure  or  the  "differential."  In 
other  words  the  "differential,"  in  cases  of  liquids,  indicates 
the  velocity. 

The  Differential  Gauge  records  on  a  chart  the  differential 
pressure  existing  between  the  pressure  connections.  This 
factor  with  the  known  area  of  the  orifice  enables  us  to  de- 
termine the  flow  of  liquids  from  the  formula : 

Q  =  C  VT 

Where  ()  =  the  Quantity  of  liquid  passing  the 
orifice.  The  result  can  be  expressed  in 
"gallons"  or  "barrels"  per  hour. 
C  =  the  Hourly  Coefficient.  The  value  of  this 
term  remains  the  same  for  each  installation 
and  basis  of  measurement. 

h  =  the  Differential  Pressure  existing  between  the 
two  pressure  connections,  expressed  in  inches 
of  water  head,  this  value  is  recorded  graphi- 
cally on  the  chart  of  the  Recording  Dif- 
ferential Gauge. 

The  value  of  the  Hourly  Orifice  Coefficient  C   in  the 
above    formula    is    found    on    Page      330,   computed    for 
various  diameters  of  orifice  and  diameters  of  pipe,   these 
values  having  been  determined  by  exhaustive  experimental 
and  practical  tests  in  comparison  with  actual  displacement. 
The  extensions  of  the  values  of  V  h  have  been  compiled  and 
are  given  in  Table  64  Page  313. 
Example — One  hour  reading: 
Average  differential  reading  h  =  25  inches. 
Diameter  of  Pipe  =  4  inches. 
Diameter  of  Orifice  =  2  inches. 

320 


MEASUREMENT      OF      OIL 


321 


MEASUREMENT      OF      OIL 


When  oil  is  measured  (using  the  above  data  with  Gravity 
30  deg.  Baume)  the  Hourly  Orifice  Coefficient  C  is  24.64  of 
a  2  inch  orifice  in  a  4  inch  line,  (Table  67,  Page  330). 

Orifice  Pressure 

(2-24.64    V25     -24.64     X     5.000 

Coefficient  Extension 

or  the  quantity  passing  through  the  orifice  =  123.2  barrels  per 
hour. 

Therefore  the  quantity  per  hour  flowing  in  the  line  is 
equal  to  the  Orifice  Coefficient  multiplied  by  the  Differential. 

The  relation  between  the  differential  and  the  velocity  of 
the  fluid  through  the  orifice  is  expressed  by  the  formula  : 


Where  V  =  velocity  of  flowing  fluid  in  feet  per  second. 

g  =  acceleration  due  to  gravity  in  feet  per  sec.,  per 

sec.  =  32.16. 

H  —  differential  expressed  in  feet  head  of  flowing 
fluid.  _ 

The  well  known  formula  V=  V2  gH  expresses  the  theoret- 
ical flow,  eliminating  friction  and  other  influences.  When 
applied  to  actual  conditions  a  correcting  factor  is  used  to 
take  care  of  influences  due  to  contraction  of  jet,  friction,  etc. 
This  correcting  factor  Cv  is  commonly  known  as  the  "co- 
efficient of  velocity." 

In  this  formula  the  differential  head  is  expressed  in  feet 
head  of  flowing  fluid  ;  and  as  it  is  not  practical  except  in  case 
of  water  to  register  this  value  directly,  the  differential  is 
recorded  on  the  chart  in  inches  of  water  pressure.  If  oil  of 
30  deg.  Baume  is  flowing  in  a  line,  the  theoretical  differential 
would  be  expressed  in  feet  head  of  oil.  The  specific  gravity 
of  this  oil  is  0.875  therefore  0.875  feet  or  lO^  inches  of  water 
would-be  equivalent  to  one  foot  of  oil.  One  inch  of  water 
equals  1/10.5  or  0.09525  feet  of  oil.  Twenty  inches  of  water 
would  equal  20  times  0.09525  feet  or  1.905  feet  head  of  oil  at 
30  degrees. 

322 


MEASUREMENT      OF      OIL 


h 


Where  #=-  differential  in  feet  head  of  flowing  fluid. 
h  =  differential  in  inches  of  water  pressure. 
12  =  number  of  inches  in  a  foot. 
p  =  specific  gravity  of  flowing  fluid  (water  =  1.000) 
The  above  example  would  be  written  thus: 
90 


12  X  0.875 


=  1.905  feet  of  head  oil. 


Substituting  the  value  of  H  in  the  formula  V  =  Cv  V  2gH 


We    obtain    V  =  CV        --      =     Cv 


2  X  32.16 


12p  12p 


7  =  2.3152  Cv^ 
p 

This  expression  illustrates  the  fact  that  the  velocity  de- 
pends upon  the  specific  gravity  of  the  liquid.  As  the  specific 
gravity  increases,  the  velocity  decreases  when  the  differential 
pressure  is  a  constant. 

Or  using  a  plain  illustration  with  the  same  force  applied, 
a  cubic  foot  of  hot  tar  will  move  with  less  speed  or  velocity 
than  the  same  quantity  of  gasoline. 

In  measuring  light  or  heavy  oils  with  an  orifice  meter  the 
connecting  lines  and  the  gauge  itself  are  filled  with  water  or 
oil  and  thus  the  heads  of  liquid  acting  on  each  portion  of  the 
gauge  are  equal. 

Due  to  the  fact  that  the  recording  gauges  are  filled  with 
liquid  each  inch  of  mercury  differential  is  partially  counter- 
balanced by  an  inch  of  liquid.  Each  inch  of  mercury  dif- 
ferential is  equivalent  to  only  (13.6-pg)  inches  of  water 
differential  instead  of  13.6  inches  which  would  be  the  case  if 
the  liquid  did  not  fill  the  gauge  and  connections. 

323 


MEASUREMENT      OF      OIL 

Where  13. 6  =  specific  gravity  of  mercury. 

pg  =  specific  gravity  of  liquid  in  gauge. 


13.6-/ 


Therefore,  the  differential  h  is  multiplied  bv  the  factor  — 

13.6 

for  the  reason  that  differential  gauges  are  constructed  to 
indicate  13.6  inches  of  water  pressure  differential  for  each 
inch  of  mercury  differential. 

Substituting  these  factors  in 

7  =  2.3152  C       — 


we  obtain 

7  =  2.3152 


13.6  p 


The  quantity  of  fluid  passing  the  orifice  in  gallons  per 
hour  is  equal  to  the  area.  of  the  orifice  in  square  inches  multi- 
plied by  the  velocity  in  inches  per  hour  divided  by  231.  This 
fact  may  be  expressed  by  the  following  formula  : 

0.7854    2 


231 

Q=  146.88  d2  X  V 

Where  Q  =  quantity  of  fluid  passing  the  orifice  in  gallons 
per  hour. 

0.7854  d2  =  area  of  orifice  in  square  inches. 
d  =  diameter  of  orifice  in  inches. 
231=  number  of  cubic  inches  in  a  gallon. 
3600  =  seconds  in  one  hour. 

y  =  velocity  of  fluid  through  orifice  in  feet  per  sec. 
12  =  number  of  inches  in  a  foot. 
324 


MEASUREMENT      OF      OIL 


325 


MEASUREMENT      OF      OIL 


MEASUREMENT      OF      OIL 


Substituting  the  value  of  V  where  7=2.3152  Cv 
in  this  expression. 

Q=  146.88  d2X 2.3152  Cv  -J(1^?g)/? 

'       lo.u  p 


13.6  P 

It  has  been  found  that  the  simple  layout  shown  on  Page 
318  can  be  used  very  satisfactorily  for  measuring  light 
oils  or  oils  of  low  viscosity. 

For  heavy  oils,  reservoirs  (Figs.  131  and  132)  made  of  a 
12  inch  length  of  4  or  6  inch  pipe  and  two  caps,  are  installed 
on  each  gauge  line.  These  reservoirs  are  installed  vertically 
on  the  same  level.  The  reservoirs  and  gauge  are  filled  with 
water.  When  oil  is  admitted  to  the  reservoirs  from  the 
main  and  when  the  gauge  is  open,  the  air  in  the  gauge  lines 
and  gauge  will  be  displaced  by  the  water.  The  excess  water  be- 
ing released  by  valves  RR.  Figs.  131  and  132,  so  that  the  water 
occupies  about  one  half  of  the  height  of  the  reservoir.  When 
the  by-pass  lines  are  open  and  a  flow  does  not  exist  through 
the  orifice,  the  surface  of  the  water  will  seek  the  same  level 
and  the  pressure  head  of  the  liquids  in  the  gauge  lines  and 
gauge  will  be  equal.  When  a  flow  exists  and  the  differen- 
tial h  increases,  the  water  level  at  S  is  lowered  and  at  T  is 
raised,  (Fig.  130)  causing  a  portion  of  the  oil  to  flow 
through  the  connection  into  the  main  at  D.  In  the  mean- 
time additional  oil  is  filling  the  reservoir  S. 


.Orifice 


mcerSea/or. 


Fig,    130— DIAGRAM  OF  ORIFICE  METER  INSTALLATION 
FOR  MEASURING  HEAVY  OIL 

327 


MEASUREMENT      OF      OIL 


When  the  oil  is  measured  without  the  installation  of  water 
seals,  the  oil  occupies  the  gauge  lines  and  gauge  itself.  In  this 
case  pg  and  p  are  equal  to  the  specific  gravity  of  the  oil  being 
measured.  Table  67  was  prepared,  using  as  a  basis,  oil  of  30 
deg.  Baume  or  specific  gravity  .875.  The  previous  formulae 
give  results  in  gallons  per  hour.  To  express  the  quantity  in 
barrels  of  42  gallons  per  hour,  of  oil  of  30  deg.  B.,  the 
formula 


Q  =  340.06  C,  d  .  becomes 

*     13. 6p 


340.06  Cvd2      [(13.6-.875)  h 
42  ^  13.6X.875 

Q-8.3728  Cvd2   VT~ 
where  Q  =  quantity  in  barrels  of  42  gallons  per  hour. 

The  Hourly  Coefficient  C  in  Table  67  is  equal  to  8.3728  Cvd2. 

The  various  multipliers  shown  in  Table  68  were  determined  by 
using  various  values  of  specific  gravities  of  liquids  for  pg  and 
p  in  the  formula  and  take  into  account  the  difference  in 
water  levels  occurring  in  various  sizes  of  reservoirs  due  to 
displacement  above  and  below  the  zero  level  occasioned 
by  the  volume  of  mercury  displaced  in  the  gauge.  See 
following  example  (Page  329)  for  use  of  multipliers. 

Investigations  and  tests  have  shown  that  the  coefficient 
of  velocity  Cv  for  water  and  oils  whose  viscosity  is  less  than 
water  is  practically  the  same  as  for  gas,  air,  or  steam.  The 
compiled  data  of  some  of  the  tests  given  on  Pages  333  and 
334,  indicate  that  there  is  no  substantial  difference.  In 
computing  the  Tables  of  Hourly  Orifice  Coefficients,  the 
values  of  CV)  determined  for  air,  have  been  used. 

328 


MEASUREMENT      OF      OIL 

The  values  of  C,  the  Hourly  Orifice  Coefficient,  for  oil  of 
30  deg.  B.  are  given  in  Table  67  on  Page  330.  These 
Coefficients  are  prepared  for  pipe  of  standard  dimensions 
(2.067,  3.088,  4.026,  6.065,  8.071  and  10.191  inches  internal 
diameter).  Coefficients  for  pipes  of  other  internal  diameters 
for  various  sizes  of  orifices  can  be  determined  as  follows. 

Example— Oil  being  measured.  40  deg.  Baume.  Vis- 
cosity, 40  seconds  Saybolt.  Water  seals,  6  inches  in  diameter, 
50  inch  gauge. 

Internal  Diameter  of  Pipe  =  3. 548  inches. 
Diameter  of  Orifice  =  2J<£  inches. 

2  2^0 

Ratio  ^  =  ^^=.6342 
3.548 

Cv  for  ratio  .6342  =  .877  (Page  210). 
Coefficient- 8.3728  Cvd2. 

=  8.3728  X  .877  X  2.25  X  2.25 

=  37.17  barrels  per  hour  for  30  deg.  Baume 
without   reservoirs. 

Revision  for  Coefficient  from  30  deg.  Baume  to  40  deg. 
Baume  including  revision  on  account  of  water  seals  and 
range  of  gauge  (Table  68)  =  1.027.  Revision  for  viscosity 
(Table  69)  =  1.020. 

Coefficient  for  above  conditions  =  37. 17X1. 027 XI. 020  = 
38.93. 


329 


MEASUREMENT      OF      OIL 


Table  67 
HOURLY  COEFFICIENTS  FOR  OIL 

Pressures  taken  2^  diameters  upstream  and  8  diameters  downstream. 

Values  of  C  in  Q  =  C  V  h     where    Q    expresses    the    quantity    of    oil    or    other 

liquids  in  Barre's   (42  gallons)    having  a  density  of  30  deg.  Baume,  passing 

through  the  orifice  per  hour. 
Size  of  meter  is  the  diameter  of  pipe  line  in  which  orifice  is  placed. 


Diam. 
of 


DIAMETER  OF  PIPE  LINE 


unnce 
Inches 

2" 

3" 

4" 

6" 

8" 

10" 

"  % 

Y* 

W 

w 

1% 
1H 

1% 
1% 

iy8 

2 

2ys 
ak 

1.322 
2.108 
3.123 
4.420 
6.080 
8.217 
10.98 
14.57 
19.24 

1.296 
2.046 
2.977 
4.106 
5.451 
7.043 
8.918 
11.13 
13.75 
16.85 
20.54 
24.94 
30.18 
36.43 
43  90 

1.285 
2.022 
2.933 
4.023 
5.299 
6.773 
8.461 
10.38 
12.56 
15.03 
17.84 
21.02 
24.64 
28.76 
33  46 

2^890 
5'  188 
8"l86 
11.  '92 
16  '44 
21.  84 
28  24 

5^138 
8*086 
11.73 
16'09 
21.  19 
27  08 

8.026 
11  '63 
15*91 
20.90 
26  62 

2^ 
21A 

2^8 

38.83 
44.97 
52  00 

35.79 

33'  83 

33.09 

2^ 
2% 
3 

3M 
3H 

60.05 
69.23 

79.76 

44.73 

55  '31 
67.89 
'    82  88 

41.51 

50  '22 
60.09 

71  28 

40.34 

48  A3 
57.40 
67  32 

3% 

100  8 

83  99 

78  31 

4 

122  2 

98  42 

90  43 

4M 

147  8 

114  9 

103  8 

41% 

178  4 

133  6 

118  6 

*\*  \^\^>\^ 

XCO\  .-(\r-i\CO\ 

Tj<  10  10  LO  10  <£ 

155.0 
179.5 
207.5 
239.5 
276.2 
317  9 

134.9 
153.0 
173.1 
195.3 
220.0 
247  5 

Ql/i 

278  0 

QY2 

311.8 

6% 

7 

714 

349.6 
391.6 
438  2 

7y2 

490.0 

See  Tables  68  and  69  for  Multipliers  for  Specific  Gravity  and  Viscosity. 
330 


MEASUREMENT      OF      OIL 


Table  68— MULTIPLIERS  FOR  HOURLY  COEFFICIENTS 

FOR  OIL  FOR  VARIOUS  SPECIFIC  GRAVITIES 

OF  OIL  WHEN  USING  WATER  SEALS  OR 

RESERVOIRS  OF  VARIOUS  SIZES. 

USED  WITH  TABLE   67 


50" 

100" 

Reser- 

Gravity 

gauge 

gauge 

50" 

100" 

50" 

100" 

voirs 

of  Oil 
Degrees 

2H"res. 
or  no 

lM"res. 
or  no 

gauge 

ga^uge 

gauge 

gauge 
6" 

unlim- 
ited 

Baume 

res. 

res. 

res. 

res. 

res. 

res. 

Area 

10 

.931 

.931 

.931 

.931 

.931 

.931 

.931 

20 

.966 

.966 

.965 

.964 

.964 

.964 

.964 

30 

1.000 

1.000 

.997 

.996 

.996 

.996 

.995 

40 

1.033 

1.033 

1.029 

1.027 

.027 

1.026 

1.026 

50 

1.065 

1.065 

1.059 

1.057 

.057 

1.056 

1.055 

60 

1.096 

1.096 

1.089 

1.087 

.086 

1.085 

1.084 

70 

1.126 

1.126 

1.118 

1.115 

.114 

1.113 

1.112 

80 

1.155 

1.155 

1.146 

1.143 

.142 

1.141 

1.140 

90 

1.184 

1.184 

1.173 

1.170 

.169 

1.168 

1.167 

100 

1.211 

1.211 

1.200 

1.197 

1.196 

1.195 

1.193 

Minimum 

distance 

8" 

12" 

6" 

6" 

4" 

4" 

2" 

between 

connect'ns 

The  reservoirs  made  of  pipe  are  installed  vertically. 

The  minimum  distance  mentioned  is  between   the   inlet  con- 
nections and  outlet  connections  of  the  reservoirs. 

Table  69— MULTIPLIERS  FOR  HOURLY   ORIFICE 
COEFFICIENTS  FOR  OIL   FOR  VISCOSITY 

USED  WITH  TABLE  67 


Viscosity 
Saybolt 
Seconds 

Multipliers 

Viscosity 
Saybolt 
Seconds 

Multipliers 

40 
50 
60 
70 
80 
100 

1.020 
1.035 
1.045 
1.052 
1.058 
1.066 

150 
200 
300 
500 
700 
1000 

1.080 
1.092 
1.107 
1.126 
1.140 
1.150 

331 


MEASUREMENT      OF      OIL 


Table  70 
HOURLY  CAPACITIES  OF  ORIFICES  FOR  OIL 

Pressures  taken  2>£  Diameters  Upstream  and  8  Diameters  Downstream. 

Capacities  expressed  in  Barrels  of  42  Gallons. 

Size  of  Meter  is  the  Diameter  of  Pipe  Line  in  which  Orifice  is  placed. 
50  Inch  Differential  Chart 


Diam. 
Orifice 
Inches 

Size  of  Meter 

Diam. 
Orifice 
Inches 

Size  of  Meter 

2" 

3" 

4" 

6" 

8" 

10" 

IA 

5.9 

5.8 

5.8 

1M 

37 

36 

36 

*A 

9.5 

9.2 

9.0 

IX 

53 

52 

52 

H 

14.1 

13.3 

13.1 

m 

74 

72 

71 

% 

19.9 

18.4 

18.0 

2 

98 

95 

94 

i 

27.5 

24.5 

23.8 

21A 

160 

152 

148 

ly* 

37.4 

31.7 

30.4 

3 

248 

225 

217 

Vi 

50.2 

40.1 

38.0 

3^ 

371 

319 

302 

i*A 

67.0 

50.0 

46.6 

4 

546 

440 

405 

1M 

88.5 

61.9 

56.3 

4^ 

796 

597 

531 

1% 

92.9 

79.9 

5 

802 

685 

2 

137 

110 

5^ 

1070 

873 

*y± 

199 

150 

6 

1420 

1110 

2y> 

201 

6U 

1390 

*"  S  & 

&A 

268 

Vf/  Z 

7 

1750 

3 

357 

7^ 

2190 

100  Inch  Differential  Chart 


Diam. 
Orifice 
Inches 

Size  of  Meter 

Diam. 
Orifice 
Inches 

Size  of  Meter 

2" 

3" 

4" 

6" 

8" 

10" 

1A 

8.4 

8.2 

8.2 

1M 

52 

51 

51 

5A 

13.4 

13.0 

12.8 

1M 

76 

74 

74 

y± 

19.9 

18.9 

18.5 

IK 

104 

102 

101 

% 

28.2 

26.1 

25.4 

2 

138 

134 

132 

38.9 

34.7 

33.6 

2y2 

227 

214 

210 

11A 

53 

45 

43 

3 

350 

318 

307 

11A 

71 

57 

54 

3^ 

525 

452 

427 

l*A 

95 

71 

66 

4 

773 

623 

573 

ll/2 

125 

88 

80 

4^ 

1126 

845 

751 

1% 

131 

113 

5 

1134 

969 

2 

194 

156 

5^ 

1520 

1240 

2M 

281 

212 

6 

2010 

1570 

2*4 

284 

6*/£ 

1970 

**  /  £i 

2% 

380 

7 

2480 

3 

505 

7y2 

3100 

For  Minimum  Capacity  deduct  50  per  cent. 
Capacity  add  50  per  cent. 

332 


and  for  Maximum 


MEASUREMENT      OF      OIL 


TESTS— MEASUREMENT  OF  OIL 

Following  is  a  summary  of  tests  conducted  for  measure- 
ment of  various  grades  of  oils  by  orifice  meter. 


Table  71 


Num- 
ber of 
Tests 

Grade 

Line 
Size 

Av. 
Time 
Tests 
(hrs.) 

Total 
Quan- 
tity 
(bbls.) 

Viscos- 
ity 
Factor 

Aver- 
age 
Devia- 
tion 

07 

Devia- 
tion of 
Total 

/c 

4 

Kerosene  Dis. 

8" 

2.2 

2,800 

1.000 

1.0 

+0.7% 

2 

Caddo  Crude 

10" 

10.0 

18,700 

1.000 

2.2 

+0.7% 

2 

Coastal  Crude 

8" 

10.0 

9,600 

1.050 

0.2 

+0.2% 

11 

Mex.  Crude 

10" 

5.9 

49,500 

1.146 

2.3 

+2.0% 

26 

Reduced  Mex- 

f 1.118] 

ican  Crude 

3" 

0.3 

475 

\   to 

2.5 

-0.9% 

[1  .  144J 

The  results  indicate  that  for  oils  having  a  viscosity  equal 
to  or  less  than  water,  the  coefficients  of  velocity  derived  for 
air  flow  can  be  used  by  applying  a  factor  for  gravity  only, 
and  when  oils  have  a  viscosity  greater  than  water  the  vis- 
cosity factor  must  also  be  applied. 

The  above  series  of  tests  was  conducted  for  the  purpose 
of  determining  whether  the  viscosity  of  oil  or  liquids  would 
require  the  use  of  a  coefficient  or  multiplier  for  liquids  of 
various  viscosities. 

The  preliminary  tests  conducted  on  Reduced  Mexican 
Crude  indicated  that  such  a  correction  factor  or  multiplier 
was  necessary.  In  order  to  determine  whether  a  multiplier 
was  necessary  for  oils  whose  viscosity  was  equal  to  or  less 
than  water,  tests  were  first  conducted  on  Kerosene  Dis- 
tillate (the  viscosity  of  which  is  less  than  water)  which 
indicated  that  a  multiplier  was  not  required.  A  like  result 
was  obtained  in  measurement  of  Caddo  Crude.  However, 

333 


MEASUREMENT      OF      OIL 


in  case  of  Coastal  Crude  it  was  found  that  the  orifice  meter 
measurement  gave  results  approximately  5  per  cent  less  than 
tank  measurement  when  the  multiplier  was  not  used.  In 
the  case  of  the  Mexican  Crude  and  Reduced  Mexican  Crude, 
greater  deviations  were  obtained.  These  deviations  for  in- 
dividual tests  were  plotted  on  a  logarithmic  diagram  against 
the  kinematic  viscosity  of  the  oil  in  question.  It  was 
found  that  these  deviations  did  not  vary  appreciably  from 
a  mean  curve  drawn  through  the  results.  From  this  curve  a 
multiplier  was  determined  for  use  with  oils  of  varying  vis- 
cosities which  multiplier  or  factor  was  afterwards  applied 
to  the  results  with  the  deviations  as  shown  above. 

In  order  to  determine  the  effect  of  pumps  on  lines  and 
relative  effect  due  to  location  of  pumps,  approximately  one- 
half  of  the  tests  were  conducted  when  the  flow  through 
the  line  was  due  to  gravity  only,  and  in  other  cases  the 
flow  was  produced  by  pumps  at  various  distances  from  the 
meter,  in  some  cases  being  only  10  feet  away  from  the  meter. 
However,  in  all  of  these  cases  the  pumps  were  double  acting 
and  made  only  about  40  revolutions  per  minute.  The  re- 
sults obtained  by  gravity  and  those  obtained  when  pumps 
were  used,  were  similar.  There  was  no  evidence  of  any  de- 
viation which  could  be  attributed  to  the  pumps.  However, 
in  the  measurement  of  gas  or  any  liquid  it  is  not  possible  to 
measure  a  flowing  liquid  where  pulsations  are  produced 
through  the  orifice  by  quick  acting  pumps. 

In  addition  to  the  above  tests,  extensive  tests  covering  a 
period  of  a  month  or  more  were  made  in  which  several  hun- 
dred thousand  barrels  of  Coastal  Crude  Oil  were  measured, 
the  results  of  which  checked  with  tank  measurement  within 
3/10  of  a  per  cent  and  at  the  same  time  tests  were  conducted 
using  the  orifice  meter  for  measurement  of  reduced  Mexican 
Crude  Oil  in  which  the  percentage  deviation  between  tank 
measurement  and  meter  measurement  was  varied  from  3/10 
of  a  per  cent  to  1^  per  cent  measuring  3800  barrels  of  oil. 

334 


MEASUREMENT      OF      OIL 


INSTALLING    AND    TESTING    OIL    METERS 

See  Figures  on  Pages  318  and  339. 

To  successfully  measure  oil  it  is  necessary  to  eliminate 
violent,  pulsation  and  vibration  from  pumps  by  means  of 
air  chambers  or  by  placing  the  meter  as  far  away  from 
pumps  as  possible. 

The  preceding  instructions  relative  to  gas:  Measuring 
Gases  and  Liquids,  Orifice  Meter  Body,  Orifice  Meter 
Flanges,  Gauge  Line  Connections  or  Taps,  Setting  up  Gauge, 
Differential  Pen  Arm,  Glass,  Adding  Mercury,  Static 
Pressure  Connections,  (Pages  239  to  248)  apply  for 
measuring  oil  with  the  following  exceptions:  In  measuring 
oil  the  installation  may  be  made  in  any  line  whether  level, 
inclined  or  vertical.  The  main  line  by-pass  and  valves  may 
be  omitted.  In  measuring  heavy  oil  it  is  desirable  to  pre- 
vent the  oil  from  entering  the  gauge  or  coming  in  contact 
with  the  mercury.  The  use  of  water  reservoirs  or  seals 
eliminate  this  possibility.  Figure  130  shows  diagram- 
atically,  oil  installations,  one  where  the  oil  line  is  above  the 
gauge  and  the  other  where  it  is  below.  The  reservoirs 
Figs.  131  and  132  should  contain  valves  or  plugs  in  the  top 
for  releasing  the  air  when  they  are  being  filled  with  water 
(Page  339).  The  valves  RR  are  placed  at  the  middle 
point  in  the  vertical  height  of  the  reservoirs  and  on  a 
level  with  each  other  for  purposes  of  determining  the  height 
of  water  in  the  reservoirs  when  the  installation  is  ready  to 
be  placed  in  operation.  Ordinary  visible  water  gauges  and 
glasses  may  be  used  in  place  of  valves  RR  to  indicate  the  level 
of  the  water  in  the  reservoirs.  The  connections  or  pipe  lines 
from  the  upstream  and  downstream  connections  to  the 
reservoirs  and  the  oil  by-pass  between  the  reservoirs,  are 
%  inch  pipe.  This  oil  by-pass  is  installed  so  that  the  head 
of  water  in  the  reservoirs  can  be  leveled  by  opening  valves 
B  and  Z  when  valves  W  and  X  are  closed.  If  the  head  of 

335 


MEASUREMENT      OF      OIL 


water  is  higher  in  one  reservoir  than  in  the  other,  the  dif- 
ferential reading  will  be  affected  due  to  the  difference  in 
densities  of  the  water  and  oil.  In  measuring  light  refined 
oils  use  the  simple  layouts  shown  on  Page  318. 

By  Pass — Install  by-pass,  placing  valve  at  Z. 

Removing  Chart,  Clock,  Placing  Chart,  Pens  and 
Ink,  Vibrating  Pen  Arm,  and  Adjustments  (Pages  248,  249, 
250  and  258) — These  articles  apply  with  the  exception  that 
the  static  spring  and  pen  arm  are  not  necessary  as  the 
liquids  are  practically  incompressible. 

Starting  Gauge — 

Fill  gauge  and  reservoirs  with  water. 

(In  measuring  light  oils  omit  reference  to 
reservoirs  and  valve  B,  when  using  layouts, 
Page  318) 

Open  B,  Z,  K  and  P 

Open  valve  W  slightly  to  admit  line  pressure 
eliminating  air  at  K  and  P.  When  all  of  air  is 
eliminated.  Open  and  close  funnel  to  release  air. 

Close  P  and  K 

Open  W 

Open  RR  until  oil  flows  from  each  valve,  or  if 
visible  gauge  glasses  are  used  release  the  water 
from  the  petcock  from  the  lower  gauge  cock  until 
the  oil  occupies  the  upper  half  of  the  reservoir, 
then  close  the  valves  or  petcocks. 

Close  B  and  Z 

OpenX 

Leaks — Stop  all  leaks. 

Orifice  Capacities  —  See  Page  298.  For  capacities  see 
Page  332. 

336 


MEASUREMENT      OF      OIL 

Checking  Differential  Gauge  for  Zero — 
Close  W  and  X 
OpenK 
Open  Z 
The  differential  pen  should  return  to  zero. 

The  differential  pen  arm  should  be  kept  in  a  straight  line. 
It  can  be  adjusted  to  zero  by  moving  slightly  at  the  joint  or  at 
the  connection  with  the  shaft.  When  the  pen  rests  at  zero, 
determine  if  the  float  is  floating  and  not  resting  on  the  bot- 
tom of  the  chamber.  (See  Page  247). 

Close  Z  and  K 

Partially  open  P 

Then  open  X  carefully  when  the  differential 
pen  should  recede  one-fourth  inch  or  more  (actual 
measurement)  below  the  zero  line.  If  the  float 
rests  on  the  bottom  of  the  chamber  at  zero,  add 
mercury.  (See  Page  247). 

After  test  close  P  and  X  and  Open  Z 

Checking  Differential  Pen  Arm — 

(In  measuring  light  oils  omit  reference  to 
valve  B,  when  using  layouts,  Page  318) 

Close  W  and  X 

Attach  a  single  column  glass  tube  with  a 
rubber  connection  and  nipple  at  tap  P  and  fasten 
tube  in  a  rigid  vertical  position.  (Page  301). 

Open  K,  Z  and  B 

Open  W  slightly  and  admit  pressure  slowly  to 
expel  air  from  K 

Mark  level  of  water  in  glass  tube  attached  to 
connection  at  P  when  water  seals  are  used. 

Close  B  and  Z 

337 


MEASUREMENT      OF      OIL 


By  opening  and  closing  W  the  reading  can  be 
checked  with  the  column  of  water  in  the  tube 
above  the  zero  mark.  One  inch  of  differential 
reading  on  the  chart  is  equal  to  0.926  inches  of 
water  head  above  the  zero  mark  in  the  water 
column. 

This  statement  applies  when  water  seals  or  reservoirs  are  used. 
(See  Table,  Page  301). 

When  using  the  layouts  for  measuring  light  oils,  Page 
318,  the  light  oil  will  fill  the  glass  tubing.  The  height  that 
it  rises  above  the  zero  setting  for  a  certain  chart  reading  will 
be  equal  to  the  water  reading  revised  for  the  gravity  of  the 
oil  according  to  the  following  Table. 


Table  72 

CHECK    READINGS    ON    LIQUID    COLUMN 
IN  INCHES  OF  LIQUID 


Be. 

Reading  on  Chart 

Be. 

Reading  on  Chart 

Grav- 

Grav- 

ity 

10" 

30" 

50" 

100" 

ity 

10" 

30" 

50" 

100" 

30 

10.7 

32.0 

53.4 

106.9 

65 

13.2 

39.6 

66.0 

131.9 

35 

11.0 

33.1 

55.2 

110.5 

70 

13.5 

40.6 

67.7 

135.5 

40 

11.4 

34.2 

57.0 

114.1 

75 

13.9 

41.7 

69.5 

139.1 

45 

11.8 

35.3 

58.8 

117.7 

80 

14.3 

42.8 

71.3 

142.7 

50 

12.1 

36.4 

60.6 

121.2 

85 

14.6 

43.9 

73.1 

146.2 

55 

12.5 

37.4 

62.4 

124.8 

90 

15.0 

44.9 

74.9 

149.8 

60 

12.8 

38.5 

64.2 

128.4 

95 

15.3 

46.0 

76.7 

153.4 

In  the  latter  case  the  oil  may  be  removed  from  the  gauge  and 
it  may  be  tested  by  filling  the  gauge  with  water,  by  closing 
W,  X,  and  Z,  opening  K  and  adding  water  through  the 
glass  tubing.  In  this  case  use  Table,  Page  301. 


338 


MEASUREMENT      OF      OIL 


Fig.  131—50  INCH  GAUGE  INSTALLATION  FOR  MEASURING  OIL 


Fig.  132—50  OR  100  INCH  GAUGE  INSTALLATION  FOR  MEASURING   OIL 

339 


MEASUREMENT      OF      OIL 

READING  CHARTS 

The  formula  for  use  of  the  orifice  meter  is : 

Quantity  of  liquid  per  hour  =  Coefficient  X  V  h  , 
in  which  h  =  differential  pressure  in  inches  of 
water. 

To  obtain  quantity,  average  the  differential  pressure  for 
each  hour  of  the  day.  Obtain  values  of  V  h  (differential 
pressure  extensions)  for  each  hour.  Add  these  extensions 
together  and  multiply  the  sum  by  the  coefficient  for  the 
orifice  being  used.  The  product  will  be  the  quantity  of  oil 
or  water  passing  through  the  meter  for  the  period  during 
which  the  differential  pressure  is  averaged. 

See    Page    313    for    a    table  of    Differential 
Pressure   Extensions,  (values  of  V  h  ,  1  to 
100  inches). 
See  Page  268,  Orifice  Meter  Calculator. 

'JVT: 

ORIFICE  METER  CHART  REPORT,. 
STATION JfasYLrt*1^  DATE 
Ho.  A-'. 


Differential  Extension 

TIME  Inches 

Water 


12  -  1  a 

1  -  2  a 

2  -  3  a 

3  -  4  a 

4  -  5  a 


,9  *°*C 


TOTAL  . 
Coeff. 


DELIVERY 


Fig.    133—  ORIFICE    METER   CHART  REPORT    FOR    A 
PERIOD    OF  5  HOURS 

340 


PART     EIGHT 

ORIFICE   CAPACITIES 


The  following  Tables  of  Hourly  Capacities  of  Orifices 
give  the  approximate  capacities  for  orifices  at  various  dif- 
ferentials, each  Table  for  a  certain  line  pressure.  They  are 
based  on  specific  gravity  .6,  pressure  base  4  oz.,  base  and 
flowing  temperature  60  deg.  fahr.,  atmospheric  pressure  14.4, 
and  are  prepared  for  ten  different  pressures  and  four  sizes 
of  line,-  40  tables  for  pressures  taken  at  the  flange  and  40  for 
23/2  and  8  diameter  connections.  The  capacities  for  pres- 
sures taken  at  the  flange  apply  where  the  static  pressure  is 
obtained  on  the  downstream  side  of  the  orifice. 

Referring  to  Table  104  for  10  inch  line,  pressure  0  lb., 
the  capacity  of  2^£  inch  orifice  at  0  pressure,  1  inch  differen- 
tial is  8000  cubic  feet  per  hour.  If  this  size  of  orifice  is  being 
used  in  connection  with  a  50  inch  gauge,  an  average  reading 
of  1  inch  is  entirely  too  small.  If  the  pressure  remains  the 
same  it  is  advisable  to  obtain  a  reading  at  least  4  inches  or 
greater  on  a  50  inch  gauge  at  this  volume  of  flow.  A  2  inch 
orifice  has  a  capacity  of  8300  feet  an  hour  at  4  inches  differen- 
tial, a  1%  inch  orifice  would  produce  a  differential  of  greater 
than  6  inches  and  a  1^  inch  orifice  a  differential  of  between  10 
inches  and  15  inches.  These  Tables  serve  to  indicate  a  proper 
size  of  orifice  required  to  obtain  a  certain  average  differential 
for  a  certain  hourly  flow.  The  relative  capacities  of  ori- 
fices where  the  line  pressure  will  be  approximately  the  same 
before  and  after  changing  the  orifice,  can  be  determined  by 
using  any  table  for  the  same  size  of  line.  If  the  pressure  is  40  lb. 
per  square  inch,  the  2%  inch  orifice  in  a  10  inch  line  at  2 
inches  differential  will  have  the  same  capacity  as  l1/^  inch 
orifice  in  a  10  inch  line  at  50  inches  differential. 

341 


ORIFICE      CAPACITIES 


If  the  hourly  rate  of  flow  is  approximately  80,000  cu.  ft. 
per  hour  for  a  4  inch  orifice  in  a  10  inch  line,  at  average  dif- 
ferential reading  of  about  20  inches  at  zero  pressure  and  it  is 
desired  to  reduce  the  Jlow  to  20,000  feet  per  hour  and  still 
obtain  the  approximate  average  of  20  inches  differential. 
By  following  the  capacities  opposite  a  20  inch  differential 
to  the  right,  (Table  104)  it  is  seen  that  the  2  inch  orifice  has  a 
capacity  of  18,600  cubic  feet  per  hour  at  zero  pressure  and  20 
inches  differential.  A  2^  inch  orifice  has  a  capacity  of  23,700 
cubic  feet  per  hour  at  0  pressure  and  20  inches  differential. 
Use  the  2  or  2J4,  preferably  a  2 J/g  inch.  It  is  shown  that  if 
the  same  size  of  orifice  is  used,  for  instance,  the  4  inch  orifice 
at  20  inches  differential  for  measuring  80,000  feet  per  hour 
the  average  differential  for  20,000  feet  per  hour  would  be 
less  than  1 J'2  inches  which  is  entirely  too  low  a  differential  for 
a  50  inch  gauge. 

The  Tables  also  show  that  a  gauge  with  a  maximum  dif- 
ferential of  10  inches  has  45  per  cent  of  the  maximum  cap- 
acity of  a  50  inch  gauge  and  that  a  20  inch  gauge  has  63  per 
cent  of  the  capacity  of  a  50  inch  gauge.  The  maximum 
range  of  gauge  to  be  used  can  be  determined  very  quickly 
by  inspection  of  a  table  showing  the  line  pressure  and  size 
of  line.  Although  these  tables  are  prepared  on  a  pressure 
base  of  4  oz.  and  specific  gravity  of  .6,  they  may  be  used  as 
above  indicated  by  remembering  that  the  relative  capacities 
of  various  orifices  for  various  differentials  are  the  same  re- 
gardless of  pressure  base  and  specific  gravity.  If  the 
specific  gravity  is  1.5,  pressure  base  3  lb.,  it  is  still  true  that 
a  4  inch  orifice  in  a  10  inch  line  at  1  inch  differential  will  have 
approximately  the  same  capacity  as  a  1%  inch  orifice  in  a  10 
inch  line  at  40  inches  differential.  These  tables  will  eliminate 
delays  in  making  calculations  to  determine  the  proper  size  of 
orifice  to  be  used  where  orifices  are  to  be  changed  on  ac- 
count of  change  of  flow,  change  of  pressure  and  excessively 
low  or  high  differentials. 

342 


ORIFICE      CAPACITIES 


The  following  table  gives  the  multipliers  for  revision 
of  the  Capacity  Tables  for  Pressure  Base  and  Specific 
Gravity. 

Table  73 

MULTIPLIERS  FOR  REVISION  OF  ORIFICE  CAPACITY 

TABLES  FOR  GAS  FOR  SPECIFIC  GRAVITY 

AND  PRESSURE  BASE 


SPECIFIC  GRAVITY 

Pressure 
Base 

.60 

.70 

.80 

.90 

1.00 

1.10 

1.20 

1.30 

1.40 

0      oz.  . 

1.02 

.94 

.88 

.83 

.79 

.75 

.72 

.69 

.67 

4      oz. 

1.00 

.93 

.87 

.82 

.78 

.74 

.71 

.68 

.66 

8      oz. 

.98 

.91 

.85 

.80 

.76 

.73 

.70 

.67 

.64 

10      oz. 

.97 

.90 

.84 

.80 

.76 

.72 

.69 

.66 

.64 

1      Ib. 

.95 

.88 

.82 

.78 

.74 

.70 

.67 

.65 

.62 

l^lb. 

.92 

.85 

.80 

.75 

.71 

.68 

.65 

.63 

.60 

2      Ib. 

.89 

.83 

.77 

.73 

.69 

.66 

.63 

.61 

.59 

3      Ib. 

.84 

.78 

.73 

.69 

.65 

.62 

.59 

.57 

.55 

Fig.  134 


343 


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t      CM  00 
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Ccb 
rH  rH  rH  CM 


rH  CO  CM  CO 
CO  lO  O5  CM 
CM  CM  CM  CO 


i>  co  QO 

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CO   rH   ^   rH 
f^HrHrHrH  i-HCV3Cv3CV> 


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C005CMTj<        LOt-05CM 


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t-'  i-H  tO  O 

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rH  CO  O  CO 
CM  CM  CO  CO 


00  CO  rH  CO 
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^^CMCO        ^COXO        ^000        0000 


380 


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CO 
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CO  £>• 

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O  LO  00  rH     Oi  rH  b- 

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O5  rH  rJ4  CO 


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rH  CO  -^ 

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381 


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t—   CO   OS   rH 


00  OS  CO         CO  CO  00  CO 
rH   rH  rH  rH  CVJ  CVJ  CVJ 


iO  rH 


00 
CO 


cv  i 

Tf  00  ^ 
CVJ  Cvj  00 


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CO   t-  OS    rH   CVJ   rH 


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OOCOrHiO         COJ>COOS 


CO  OS  CO  00 
rH   00  l>  O 

CVJ  Cvj  Cvj  00 


CO  rH  rH  O         CO 


rH  OS  CO  CO         O  00 


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CO  rH  00         rH  rH 

CO  CO  OS  O  rH 


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CO  10  10  CVJ 

Cvj  CVJ  00  00 


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rHrHCVJOO          rH  CO  00  O          «  O  O  O          0000 


382 


ORIFICE      CAPACITIES      FOR      GAS 


PQ 


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«  fi 
o  * 


CO 


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js  P=^  :  -a 


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Tj<  CO 


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CD  CM  i>  10 
C\J  CO  CO  TH 


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CO  O  i—  1  CO 
CO  O  CO  00, 
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OJ  CO 


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CO 


55 


i-i  l>  d  OJ 
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OS  OJ 

rH  OJ 


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l>  rH  IO 

OJ  CO  CO 


t-OrHO  Ot-COO  OJrH 

tO  t>  CO  OS    rH  OJ  10  00    OOl 


CO  ^  t-  00 
W  OJ  CO  00 


00 

^  to  CD  t^ 


CO 
iO 


O  00  O  rH    OS  IO  OS 


rH  CO  CO  CD 

OJ  10  t>  -H 

rH  rH  rH  OJ 


O  CO  CO  lO 

to  o  to  os 

OJ1  CO  CO  00 


CD  CO  OJ  O 

06  d  oj  to 


CO  OJ  rH  CO    tO  CD  CO 


OOOOi>tO         rHt>l>CD 
OOCOrHiO         COCOJ>OO 


rHrHOJCO         rHCOOOO 


o  o  o  o 

tO  CO  000 


383 


ORIFICE      CAPACITIES      FOR      GAS 


Table  114 
4  INCH  LINE  HOURLY  CAPACITIES  OF  ORIFICES  PRESSURE  0  LB. 

Specific  Gravity  .600  Pressure  Connections  at  Flange.  Pressure  Base  4  oz. 
Base  and  Flowing  Temperature  60  deg.  fahr.  Atmospheric  Pressure  14.4  Ib. 

All  capacities  expressed  in  thousands  of  cubic  feet. 

Diameter  of  Orifice  in  Inches 

CO 

IO  CO  O  rH 
CO*  rH  id  CO* 

rH  OS  b-  O 
b-'  t-  CO  O 

rH 

•H  b-  CO  rH 

•H  co  id  os 

rH  rH  rH  rH 

CM  OJ  CO  00 

rH 

CO  O  rH  rH  OS 

rH  10  CO  b-  b- 

CM 

fO^rHrH 

CD  CM  00  OS 

CO  CO  rH  CM 

CO  CD  OS  CO 

•H  rH  CM 

CM  CO  CO  rH 

IO  CO  CO  b- 

CO  O  CM  iO 

rH  rH  rH 

rH  CM  CM  CM 

rH  OS  CO  CD  CM 
CO  CO  rH  iO  CD 

CM 

CO  b-  OS  00 

rH  CO  O  b- 

CM  CM  CO  CO 

CO  00  CO  CM 
rH  rH  lO  CO 

OS  IO  CO  O 

CO  CO  OS  CM 

rH 

00  OS  iO  00 

CO  CD  OS  rH 
rH  rH  rH  CM 

b-  OS  CO  CD  00 

CD  O  b-  CO  00 
CM  CO  CO  rH  rH 

CM 

OS  b~  OS  CO 

CD  O  CO  OS 

rH  CM  CM  CM 

00  00  rH  OS 
CO  b-  rH  b- 

00  CO  rH  rH 

CO  CO  CO  CO 

id  co  i>  os 

b-  rH  rH  OS 

o  co  id  co 

rH  rH  rH  rH 

b-  OS  CO  CO  CO 
CM  CM  CM  CO  CO 

CM 

OS  CO  CM  CO 
CM  lO  CO  CM 

888rH-g 

O  00   rH 

CM  O  IO  OS 

CO  CM  CO  00  00 

rH  rH  rH  CM 

CM  CM  CO  CO 

r^lOb- 

CO  O  rH  CM 

10  00  CM  10  CO 

CM  CM  CM 

S 

CO  O  00  OS 
OS  CM  CO  CO 

10  CO  05  CO 
OS  rH  CO  b- 

OS  00  b- 
O  b-  CO  rH 

CM  CO  b-  CO 
CO*  b-  CO'  OS 

O  00  OS  lO  00 
CM  CO  CD  OS  rH 

•H  rH  rH  rH  CM 

rH  rH  rH 

rH  CM  CM  CM 

CO  CO  rH  lO 

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rH 

rH  CO  rH  rH 

b-  CO  O  CM 

r?8£2 

CO  b-  O  rH 
CM  b-  CM  OS 

CM  CM  CO  CO 

2^10  rHrH 

rH  id  CD  b-^ 

CO  rH  rH  CO  O 

CO  O  CM  rH  CD 

rH  rH  rH  rH 

rH  rH 

rH  rH  rH  CM 

rH 

o  -H  o  co 

iO  CD  b-  CO 

83^3 

SSs-clb? 

Sg^C? 

rH  O  CO  O  rH 

CO  CO  rH  rH 

CD  b-  CO  O  rH 

rH   rH 

rH 

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rH  OS  IO  lO 
CO  CO  rH  lO 

"££8?  2 

CO  b™  b™  OS 

rH  rH  rH  rH 

CM  b-  CD  OS 
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CM  CM'  CM  CO 

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CO  rH  iO  CO  b- 

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CO  rH  O  OS 
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fcSSS? 

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OS  rH  CM  00  rH 

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rH  rH  CM  CM 

CM  CO  rH  rH  iO 

X 

O  rH  »O  CM 
CO  CM  10  rH 
rH  CM  CM  CO 

rH  CO  CM 
CD  O  rH  rH 
CO  rH  -^H  iO 

b-  O  rH  OS 
iO  b-  CO  OS 

rH  O  rH  O 
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rH  IO  CM  rH  CO 
CM   10   rH   CD   O 

rH  rH  rH  rH           CMCMCOCOrH 

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CO  Ti<  10  CO 

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CM  CD  kO  OS  CO 
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88  S  8 

CO  CO  CO  O  05 
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Differential 
in  Inches 
of  Water 

oSoo 

5S§8 

10 
rH  rH  CM  CO 

rH  CO  00  O 

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384 


ORIFICE      CAPACITIES      FOR      GAS 


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CO  OS  CM  rH 

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CM  CM  00  CO 

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385 


ORIFICE      CAPACITIES      FOR      GAS 


os  CM  n<  oj 

CO  r-H  rH  OS 

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ORIFICE      CAPACITIES      FOR      GAS 


Table  134 
8  INCH  LINE  HOURLY  CAPACITIES  OF  ORIFICES  PRESSURE  0  LB. 

Specific  Gravity  .600  Pressure  Connections  at  Flange.  Pressure  Base  4  oz. 
Base  and  Flowing  Temperature  60  deg.  fahr.  Atmospheric  Pressure  14.4  Ib. 
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Table  145 
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Specific  Gravity  .600  Pressure  Connections  at  Flange.  Pressure  Base  4  oz. 
Base  and  Flowing  Temperature  60  deg.  fahr.  Atmospheric  Pressure  14.4  Ib. 
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423 


ORIFICE      CAPACITIES 


ORIFICE  CAPACITY  DIAGRAMS 

The  orifice  capacity  diagrams  shown  on  Pages  426  and  427 
will  be  found  useful  in  determining  the  proper  size  of  orifice  to 
be  used  where  the  orifice  in  the  line  is  indicating  too  low  or 
too  high  a  differential,  and  in  cases  where  the  flow  is  to  be 
increased  or  decreased.  These  diagrams  can  be  used  to  ad- 
vantage where  the  pressure  remains  practically  the  same,  or 
where  it  does  not  vary  over  a  limit  of  20  per  cent.  As  an 
example,  we  will  assume  that  a  6  inch  line  contains  a  3  inch 
orifice  where  the  differential  pressure  averages  3  inches  on  a 
50  inch  gauge.  In  order  to  obtain  more  accurate  results  the 
differential  should  average  around  20  inches.  By  drawing 
a  line  from  coefficient  line  C  where  the  size  of  orifice  is  in- 
dicated, to  3  inch  differential  on  differential  line  D  the  inter- 
section will  be  about  14,200  on  line  Q.  Then  by  drawing  a 
line  from  20  inch  differential  at  line  D  through  the  intersection 
of  the  first  line  and  line  Q  until  the  second  line  intersects  with 
line  C  it  will  be  noted  that  the  nearest  size  of  orifice  for  a  6 
inch  line  is  2  inches  so  that  a  Q"  X  2"  orifice  at  20  inches  differ- 
ential will  have  approximately  the  same  capacity  per  hour 
at  a  certain  pressure  as  a  3  inch  orifice  at  3  inches  differential. 
As  a  further  example,  assume  that  a  6"  X  1M"  orifice  with 
connections  at  the  Flange  produces  a  differential  of  10  inches. 
By  drawing  a  line  from  line  C  to  line  D  at  the  inter- 
section on  line  Q  is  approximately  8000.  We  will  assume 
that  the  flow  through  the  line  was  20,000  cu.  ft.  per  hour  and 
that  the  proposed  flow  is  to  be  50,000  cu.  ft.  per  hour  at 
approximately  the  same  pressure.  Therefore  the  increase  in 
flow  will  be  2J/2  times  so  that  on  the  diagram  we  would  draw 
a  line  from  an  average  differential  20  inches,  on  line  D, 
through  20,000  on  line  Q,  (20,000  =  2^X8,000)  to  inter- 
section with  line  C,  which  indicates  an  orifice  6'/X2^'/. 

The  quantities  on  line  Q  are  relative  only  and  do 
not  refer  to  cu.  ft.,  gallons  or  any  particular  units.  These 
diagrams  may  also  be  used  for  water  or  oil  by  always  re- 

424 


ORIFICE      CAPACITIES 


membering  that  the  numbers  shown  along  the  line  Q  are 
relative  quantities  only.  In  the  same  manner  as  in  the  first 
example  if  a  6  inch  line  contains  a  3  inch  orifice  measuring 
oil,  water  or  steam  at  3  inches  and  it  is  desired  to  increase 
the  average  differential  to  20  inches,  the  size  of  the  new  orifice 
would  be  6"X2".  If  the  proposed  flow  and  differential  are 
both  increased  as  in  the  second  example,  the  same  relative 
sizes  of  orifice  will  be  used,  or  the  6"X1%"  orifice  will  be 
increased  to  a  6"X23/g"  orifice.  Either  of  the  diagrams  may 
be  used  for  determining  the  proper  size  of  orifice  on  account 
of  the  change  of  quantity  or  change  of  differential.  Care 
should  be  used  that  the  diagram  for  the  proper  pressure 
connections  shall  be  used. 


INFORMATION   TO   BE  FURNISHED  WHEN  ORDER- 
ING   ORIFICE    METERS    AND    DIFFERENTIAL 

GAUGES 
Measurement   of    Gas   and  Air. 

1 .  Estimate  of  maximum  rate  of  flow  in  cu.  ft.  per  hour. 

2.  Estimate  of  minimum  rate  of  flow  in  cu.  ft.  per  hour. 

3.  Approximate  maximum  line  pressure  in  Ib.  per  sq.  in. 

4.  Approximate  minimum  line  pressure  in  Ib.  per  sq.  in. 

5.  Specific  Gravity  of  gas  (Air  =  1.00). 

6.  Internal  diameter  of  pipe  line,  if  not  standard  or  if 
it  is  12  inches  or  larger,  give  actual  inside  diameter. 

7.  Pressure  Base  at  which  gas  is  to  be  measured. 

Measurement  of  Steam 

1.  Estimate  of  maximum  rate  of  flow  in  pounds  or 
horse  power  per  hour. 

2.  Estimate  of  minimum  rate  of  flow  in  pounds  or 
horse  power  per  hour. 

3.  Approximate    maximum    line   pressure    in    pounds 
per  square  inch. 

425 


ORIFICE      CAPACITIES 


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427 


ORIFICE      CAPACITIES 


4.  Approximate  minimum  line  pressure  in  pounds  per 
square  inch. 

5.  Internal  diameter  of  pipe  line,  if  not  standard,  or 
if  12  inches  or  larger  give  actual  inside  diameter. 

Measurement  of  Water 

1 .  Estimate  of  maximum  rate  of  flow  in  gallons  per  hour. 

2.  Estimate  of  minimum  rate  of  flow  in  gallons  per  hour. 

3.  Approximate  line  pressure. 

4.  Internal  diameter  of  pipe  line,  if  not  standard  or  if 
12  inches  or  larger  give  actual  inside  diameter. 

Measurement  of  Oil 

1 .  Estimate  of  maximum  rate  of  flow  in  barrels  per  hour. 

2.  Estimate  of  minimum  rate  of  flow  in  barrels  per  hour. 

3.  Approximate  line  pressure. 

4.  Specific  Gravity  of  Oil  or  degrees  Baume. 

5.  Viscosity. 

6.  Kind  of  Oils. 


428 


INDEX 


PAGE 

Absolute  Pressure 34 

— Absolute  Temperature     57 

—Vacuum  Table 43 

Absolute  Temperature.  ...     51 

— Absolute  Pressure 57 

Acceleration 45 

Accuracy  of  Orifice  Meter.   121 

Adding  Mercury 247 

Adjustment,    Differential 

Gauges 258 

Air — Derivation  of,  Form- 
ula for  Flow  of 79,163 

—Hourly  Orifice  Coeffi- 
cients, Pipe  Connec- 
tions— Pb  14.4 173 

— PbU.7 181 

— Pressures  at  Flanges  213 

—Installations  251-254 

—Meters,  Installing 239 

—Orifice     Capacities- 
Flange  Connections.  .  .   216 
— Pipe  Connections .  .  .   214 
—Testing   Differential 
Gauges . 


Ill 
75 
32 


— Velocity    Formula    for 

Flow  of 

Areas  of  Orifices 

Atmospheric  Pressure 

— Changes,  Multipliers 

for 189-196 

—Effect  of,  on  Gas  Meas-  ^ 

urement 221 

—Gas  Fields 35 

B 

Barometer 33 

Barometric  Pressure,  Abso- 
lute Pressure  Table ...     43 
—Effect  on  Gas  Measure- 
ment    221 

— Vacuum ,  ,  , 43 


Barometric  Pressure 
Changes,  Multipliers 
for 189-196 

Base,  Pressure 44 

—Multipliers 188-195 

Base  Temperature 52 

—Multipliers 191-197 

Bombshell  Type  of  Differ- 
ential Gauge  14 

Boyle's  Law 55 

By-Pass 248 


Calculator,  Orifice  Meter.  .   267 
Capacities,  Differential 

Gauge 126 

Capacities,      Orifice,      Air, 

Pipe  Connections.  .214-219 
— -Air,     Flange     Connec- 
tions  .216-249 

— Gas,  Pipe  Connections 

214,  215,344-383 

— Gas,    Flange    Connec- 
tions  216,  217,384-423 

—Oil 332 

—Steam 291 

—Water .  . 314 

Charles'  Law 53 

Charlottenburg  Tests 98 

Charts — Changing,    Orifice 

Meter 152 

— Reading — Air  and  Gas .   261 

—Oil 340 

—Steam 305 

—Water 317 

Chart  Report 265 

Clock 248 

Coefficients — Derivation — 

Air  and  Gas 79-166 

—Oil 322 

—Steam 272 

—Water 309 

— Determination  of.....     77 


429 


INDEX 


Coefficients — Continued     PAGE 
— Gas    and    Air,    Flange 

Connections 213 

— Hourly  Orifice  —  Gas 
and  Air,  Pipe  Connec- 
tions   173-184 

—Oil 330 

—Steam 282-287 

—Water .  .  312 

— Multipliers  for  revision 

of 186 

—Velocity— 50-171 

—Diagrams 108-109 

— Flange    Connec- 
tions, Table 211 

— Pipe     Connec- 
tions, Table 208 

Coke    Oven    Gas,     Orifice 

Meter  for 246 

Combination  Gauge 129 

Compressibility  of  Gases.  .     25 
Connections,    Gauge 

Line 135,245 

Constitution     of     Matter, 

Theory  of 19 

Contracts,  Gas 230 

Critical  Temperatures  and 
Pressures  of  Various 
Gases,  Table 21 


Differential  Gauges — 

Continued  PAGE 

— Portable  Gauges  for 
Testing 159 

— Recording  Differential 
Pressure  and  Tempera- 
ture    132 

—Sectional  View  of 119 

— Temperature  Effect  on  120 

—Testing— Gas  and  Air.  255 

—Oil 335 

—Steam 296 

—Water 316 

Differential  Pen  Arm 247 

—Vibrating 250 

Differential  Pressure — Ex- 
tensions for  Oil  and 
Water 313 

—Vs.  Static  Pressure.  .    .   132 


Equivalents,    Pressure, 

Table 31-32 

Erie  Holder  Tests . .  . 99 

Expansive  Power  of  Gases .     26 


Derivation   of   Coefficients 

—Gas  and  Air 79,163 

—Oil 322 

—Steam 272 

—Water 309 

Differential   Gauges — Cap- 
acities     126 

— History  of 11 

—Indicating 130 

— Installing,  (see  Install- 
ing and  Installation) 

—2^  Inch 129 

— Mercury  Float  Type ...   117 
— Ordering,    Information 

required 425 

— Permanent  Gauges  for 

Testing 158 

—Pocket  Gauge  for  Test- 
ing    156 


Filing  Orifice  Meter  Charts, 
Form  of  Face  of  En- 
velope    270 

Flange  Connections 135 

Flowing     Gases,     Velocity 

Head  of 64 

Flowing  Temperature  Mul- 
tipliers for  Changes 

of 192-198 

Fluids— 19-20 

—Pressure  of 22 

—Velocity  of 47 

Formula,    Derivation    of — • 

—Air  and  Gas 79, 163 

—Oil 322 

—Steam 272 

—Water 309 

Friction  Loss 136 

—Capacity 139 

—Percentage  of 136 

Full  Flow  Connections .  .    .134 


430 


INDEX 


PAGE 

Gas — Comparative    Meas- 
urements   219 

— Compressibility 25 

—Contracts 230 

— Expansive  Power  of .  .  .     26 
— Orifice    Capacities    for 
Flange  Connections... 

217,384-423 

— Pipe  Connections  . . 

215,  344-383 

— Orifice  Meter  Formula 

for 80,163 

—Perfect 53 

—Law  of 59 

Gauges,  Differential — Cap- 
acities    126 

— Checking  for  zero 255 

— History  of 11 

—Indicating   Flow 130 

— Information     required 

when    ordering 425 

— Installing  —  Gas  and 

Air 247 

—Oil 335 

—Steam 296 

—Water 316 

— Mercury  Float  Type ...   1 17 

—Ordering 425 

— Permanent  Gauges  for 

Testing 158 

— Temperature  Effect  on  120 
— Testing,  for  measuring 

Gas  and  Air 255 

—Oil 335 

—Steam 296 

—Water 316 

Gauges — 

— Indicating 130 

— Pressure 36 

—Setting  up 247 

—Siphon 157 

—Special  Types  of 129 

—Spring 36 

Glass : 247 

Gravitation 22 

Gravity,  Force  of 22 

Gravity,  Specific— 186 

— Multipliers  for  Changes 

of 193-199 

—Oil,  Multipliers 331 


H 

PACK 

Head — Pressure  and  Liquid    28 

—Velocity— 46 

— of  Flowing  Gases.  .     64 
History,  Orifice  Meter  and 

Differential  Gauge.  ...     11 

Holder— Erie,  Tests 99 

— Joplin,  Tests 78 

Horse  Power,  Ib.  from  and 

at  212  deg.  fahr 289 

Hourly   Capacities  of  Ori- 
fice— Gas  and  Air 

214-217,  344-423 

—Oil 332 

—Steam 291 

—Water 314 

Hourly  Orifice  Coefficients 
—Gas  and  Air.  .  .171, 184,  213 

—Oil 330 

—Steam 282,287 

—Water .  312 

Humidity    Factors 87 

I 

Indicating     Gauge 130 

Information  required  when 
ordering    Meters    and 

Gauges 425 

Ink  and  Pens 249 

Inspector's  Test  Pump  for 

Static  Pressure  Gauges  154 
Installation— Diagrams  for 

Measuring  Steam 303 

—Multiple  Orifice  Meter .  236 
—Oil  Meter,  Diagrams .  .  339 
— Orifice  Meter  for  Meas- 
uring Gases 241 

— Pitot  Meter 6 

—Water  Meter,  Diagram  318 
Installing  Differential  and 

Static  Pressure  Gauges  247 
Installing  Meters — Gas  and 

Air 239 

—Oil 335 

—Steam 2-% 

—Water 316 

Instructions  to  Meter  At- 
tendants..     152 


Joplin  Holder  Tests 78 


431 


INDEX 


PAGE) 

Law — Boyle's 55 

—Charles' 53 

—Pascal's 27 

—Perfect  Gases 59 

Layout,  Orifice  Meter 69 

Leakage  Tests— Erie  Hold- 
er    101 

— Joplin  Holder 83 

Leaks  in  Installations 249 

Liquid  Head  and  Pressure.     28 
Liquids,  Fluids  and  Gases.     20 

Loss— Friction 136 

— Pressure .  .  .141 


M 

Matter— States  of 19 

— Theory  of  Constitution 

of 19 

Measurement  —  Compara- 
tive Gas 219 

— Effect  of  Atmospheric 

Pressure  on  Gas 221 

—Flow  of  Fluids 110 

—Gases,     Orifice    Meter 

Installations  for 241 

—Oil,  Tests 333 

— Steam,  Sizes  of  Orifices 

for 293 

— Steam,  Tests 294 

—Water,  Tests 315 

Mercury,  Adding 247 

Mercury  Float  Type   Dif- 
ferential Gauges 117 

Meter,  Orifice 1 

— Accuracy  of 121 

—Adaptability  of 17 

—Body 76 

—Calculator 267 

—Chart  Report 265 

—Coefficients     (See    Co- 
efficients) 

—Coke  Oven  Gas 246 

— Derivation  of,  Formula 
for  Flow   of — Air   and 

Gas 79,163 

—Oil 322 

—Steam 273 

—Water..  .  309 


Meter,  Orifice — 

Continued  PAGE 

—Flanges 245 

—Formula  for  Gas 80 

—History  of 11 

—Installing  (See  Install- 
ing and  Installation)    . 
—Multiple  Installation      236 

— Ordering 425 

—Test Report..  ...   259 

Meter,    Pitot— Installation      6 

— Operation 6 

Multipliers — 'Atmospheric 

Pressure  Changes.  .189,  196 
— Base   Temperature 

Changes 191,197 

— Changes     of     Flowing 

Temperature 192,  198 

— Change      of      Pressure 

Base 188,195 

— Revision  of  Coefficients  186 
— Specific  Gravity  of  Gas 

193, 199-200 
—Specific  Gravity  of  Oil .   331 


Oil — Capacities    of    Orifice 

for 332 

—Coefficients  for 330 

— Measurement  Tests  .  .  .   333 
Oil  Meters,  Installing  and 

Testing 335 

Oliphant  Pitot  Tube 3 

Orifice  Areas 75 

Orifice  Coefficients,  Deter- 
mination of 77 

— Hourly — Gas    and    Air 

171-185,  213 

—Oil 330 

—Steam 282,287 

—Water 312 

Orifices 73 

— Sizes     for     Measuring 

Steam 293 

— Hourly  Capacities,  Gas 
and  Air. ..  .214-217,  344-423 

—Oil 332 

—Steam 291 

—Water.  .  .  314 


432 


INDEX 


PAGE 

Orifice  Meter 1 

— Accuracy  of 121 

—Adaptability  of 17 

—Body 76 

—Calculator 267 

—Changing  Charts 152 

—Chart  Report 265 

—Charts,  Form  for  Face 

of  Envelope  for  Filing.  270 
—Coefficients     (See    Co- 
efficients) 

—Coke  Oven  Gas 246 

— Derivation  of,  Formula 

for  Flow  of  Air 79 

—Flanges   245 

— Formula  for  Gas 80 

—History  11 

— Installations  (See  In- 
stallation and  Install- 
ing) 

—Layout 69 

—Multiple    Installation.  236 

—Test..                              .  259 


Pascal's  Law 27 

Pen  Arm — Vibration    of...   145 

—Vibrating  Differential.  250 

Pens  and  Ink  249 

Perfect  Gases 53 

—Law  of 59 

Permanent  Gauges  for  Test 

ing  Differential  Gauges .  .    158 
Pipe  Connections 135 

—Coefficients     (See    Co- 
efficients) 

— Coefficient  of  Velocity 

108-109,  208-212 

— Orifice    Capacities    for 

Air  and  Gas  214-217,344-383 
Pitot  Meter — 'Installation.       6 

— Operation 6 

Pitot  Tip  and  Box 5 

Pitot  Tube  and  Meter 2 

Pitot  Tube,  Oliphant 3 

Pocket  Gauge  for  Testing 

Differential  Gauge 156 

Portable  Pitot  Tip  and  Box      5 
Portable  Water  Differential 
Test  Gauges 159 


PAGE 
Power  of  Gases,  Expansive    26 

Pressure — Absolute 34 

— Atmospheric — 32 

—Effect  of,    on  Gas 

Measurement 221 

— M ultipliers    for 

Change 189,  196 

—Of  Gas  Fields 35 

—Base 44,  188,  195 

— Connections  or  Taps.  .   135 
— Equivalents,  Table.  ...     31 

— Gauges 36 

—Head  of  Gas 62,63 

—Liquid  Head 28 

—Loss 141 

—Static 39 

Pressure  Base,  Multipliers 

for  Change  of 188 

Pressure  Connections 135 

—Static 248 

Pressure    Extensions,    Dif- 
ferential   for    Oil    and 

Water 313 

Pulsating  Flow 143 

— Determination 147 

Pulsation 146 

Pulsation  vs.  Vibration.  .  .  .   145 
Pump,  Inspector's  Test,  for 

Static  Pressure  Gauges  154 
Pump,  Vacuum  Gauge  Test  155 


Range,  Differential  of 

Gauges 126 

Reading  Charts 261-305-340 

—Calculator 267 

Recording  Differential  and 
Static  Pressure  and 
Temperature  Gauge.  .  .  132 

Relation     Differential     to 

Pressure 132 

Relationship  between  Sta- 
tic Pressure  and  Loca- 
tion of  Orifice 134 

Report  Orifice  Meter  Chart  265 

Revision     of     Coefficients, 

Multipliers  for 186 


433 


INDEX 


PAGE 

Saturated   Steam,    Proper- 
ties of 277 

Setting  up  Gauge 247 

Siphon  or  U  Gauges 157 

Special  Types  of  Gauges  .  .   129 

Specific  Gravity 186 

—Multipliers....  193,  199,  200 

—Multipliers  for,  Oil 331 

Specific  Gravity   Changes, 

Multipliers  for 193 

Specifications     for    Orifice 

Meter  Computations .  .  202 

Spring  Gauges 36 

States  of  Matter 19 

Static   Pressure 39 

Static  Pressure  Gauges,  In- 
spector's Test  Pump  for  154 

—Installing 247 

Static  Spring,  Testing 258 

Steam,    Hourly   Capacities 

of  Orifices 291 

—Hourly   Orifice    Coeffi- 
cients  282,  287 

—Properties  of,  Table ...  277 
—Tests .  .  .294 


Taps  or  Pressure  Connec- 
tions     135 

Temperature 51 

—Absolute 51 

— Absolute  Pressure 57 

Temperature  Base 52 

Temperature  Effect  on  Dif- 
ferential Gauges 120 

Testing  Apparatus 154 

Tests 11,  13 

—Erie  Holder 99 

— Joplin  Holder 78 

—Leakage,  Erie  Holder.  .  101 
— Leakage,  Joplin  Holder  83 

—Oil  Measurement 333 

—Orifice  Meter,  Report  .  259 
— Steam  Measurement.  .  294 
— Water  Measurement. .  .  315 


PAGE 

TestingDifferential  Gauges, 

Permanent  Gauges  for.   158 

—Pocket  Gauge  for 156 

—Portable  Gauge  for. ...   159 

Testing — Gas       and       Air 

Meters 255 

—Oil  Meters 335 

—Static  Spring 258 

—Steam  Meters 296 

—Water  Meters 316 

Theory  of  Constitution  of 
Matter 19 

Tube,  Pitot  and  Meter $ 

— Oliphant 3 


V 

Vacuum 39 

— Absolute    Pressure, 

Table 43 

Vacuum  Gauge  Test  Pump  155 

Vapor 21 

Vapor  and  Gas,  Distinction 

between 21 

Velocity 44 

Velocity  Head 46 

— Flowing  Gases 64 

Velocity,  Fluid 47 

Velocity,  Coefficient  of.  .50, 171 
— Pipe  Connections 

108,  208 

— Flange  Connections ...  211 
Vibration    of    Differential 

Pen  Arm 145,250 

Viscosity,   Multipliers  for, 

Oil..  .  331 


w 

Water,  Hourly  Orifice  Co- 
efficients for 312 

Water  Measurement  Tests .  315 

Water  Meter  Installations, 

Diagram 318 

Water  Meters,  Installing 

and  Testing 316 


434 


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